Solve 8x^2+12x

$$8 x ^ { 2 } + 12 x$$

Factor

$$4x\left(2x+3\right)$$

Solution Steps

Factor out 4.

$$4\left(2x^{2}+3x\right)$$

Consider 2x^{2}+3x. Factor out x.

$$x\left(2x+3\right)$$

Rewrite the complete factored expression.

$$4x\left(2x+3\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$8x^{2}+12x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-12±\sqrt{12^{2}}}{2\times 8}$$

Take the square root of 12^{2}.

$$x=\frac{-12±12}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-12±12}{16}$$

Now solve the equation x=\frac{-12±12}{16} when ± is plus. Add -12 to 12.

$$x=\frac{0}{16}$$

Divide 0 by 16.

$$x=0$$

Now solve the equation x=\frac{-12±12}{16} when ± is minus. Subtract 12 from -12.

$$x=-\frac{24}{16}$$

Reduce the fraction \frac{-24}{16} to lowest terms by extracting and canceling out 8.

$$x=-\frac{3}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{3}{2} for x_{2}.

$$8x^{2}+12x=8x\left(x-\left(-\frac{3}{2}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$8x^{2}+12x=8x\left(x+\frac{3}{2}\right)$$

Add \frac{3}{2} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$8x^{2}+12x=8x\times \frac{2x+3}{2}$$

Cancel out 2, the greatest common factor in 8 and 2.

$$8x^{2}+12x=4x\left(2x+3\right)$$

Evaluate

$$4x\left(2x+3\right)$$