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Factoring (or factorizing) is one of the ways to solve quadratic equations, like the quadratic formula and completing the square.

The standard form of a quadratic equation is $$a{x}^2+bx+c=0$$ , in which $$a$$, $$b$$ and $$c$$ represent the coefficients and $$x$$ represents an unknown variable.

For example:
$$2x^2+7x+3=0$$

Factoring quadratics is a method of rewriting a quadratic equation in its factored form (a form of its linear factors):
$$2x^2+7x+3=\left(x+3\right)\left(2x+1\right)$$

Since both sides are equal (they are the same equation written in a different format), that means that the factored form equation also equals zero:
$$\left(x+3\right)\left(2x+1\right)=0$$

The equation's factored form allows us to find the variable values that would make the equation true. Or, in other words, finding the roots of the quadratic equation.

When the product of two factors equals zero, one or both equals zero. So we can set each of the factors to zero and solve for the variable:
$$\left(x+3\right)=0$$
$$\left(2x+1\right)=0$$
Solving these two linear equations will give us the roots for the quadratic equation:
$$x=-3$$
$$x=-1/2$$
To distinguish between the roots, write the $$x$$ as:
$$x_1=-3$$
$$x_2=-1/2$$
It is important to note that not all quadratic equations can be factored. In such cases, we need to use another method, such as the quadratic formula, to solve them.

Related terms:

Factor – a number or expression that divides another number or expression evenly, with no remainder. When multiplying two numbers or expressions, we get a product. The numbers or expressions we are multiplying are called the "factors" of that product.

Coefficient – a number used to multiply a variable. In the standard form of a quadratic equation $$a{x}^2+bx+c=0$$ , $$a$$, $$b$$ and $$c$$ are coefficients. Although $$c$$ is a constant, it is sometimes referred to as a coefficient in this context.

Splitting the middle term – a method for factoring quadratic equations. Tiger uses this method for solving quadratic equations by factoring.

Perfect square – the product of a number or expression multiplied by itself. A squared number or expression. For example, $$9$$ is a perfect square ($$9=3^2=3·3$$). $$4x^2$$ is also a perfect square ($$4x^2={\left(2x\right)}^2=2x·2x$$)

Enter your quadratic equation into Tiger's calculator. The step-by-step solution will help you understand how to solve quadratic equations by factoring.