Solve 18x^2+12x

$$18 x ^ { 2 } + 12 x$$

Factor

$$6x\left(3x+2\right)$$

Solution Steps

Factor out 6.

$$6\left(3x^{2}+2x\right)$$

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

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

Rewrite the complete factored expression.

$$6x\left(3x+2\right)$$

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.

$$18x^{2}+12x=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}}}{2\times 18}$$

Take the square root of 12^{2}.

$$x=\frac{-12±12}{2\times 18}$$

Multiply 2 times 18.

$$x=\frac{-12±12}{36}$$

Now solve the equation x=\frac{-12±12}{36} when ± is plus. Add -12 to 12.

$$x=\frac{0}{36}$$

Divide 0 by 36.

$$x=0$$

Now solve the equation x=\frac{-12±12}{36} when ± is minus. Subtract 12 from -12.

$$x=-\frac{24}{36}$$

Reduce the fraction \frac{-24}{36} to lowest terms by extracting and canceling out 12.

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

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{2}{3} for x_{2}.

$$18x^{2}+12x=18x\left(x-\left(-\frac{2}{3}\right)\right)$$

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

$$18x^{2}+12x=18x\left(x+\frac{2}{3}\right)$$

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

$$18x^{2}+12x=18x\times \frac{3x+2}{3}$$

Cancel out 3, the greatest common factor in 18 and 3.

$$18x^{2}+12x=6x\left(3x+2\right)$$

Evaluate

$$6x\left(3x+2\right)$$