Solve -6a-18a^2=

$$- 6 a - 18 a ^ { 2 } =$$

Factor

$$-6a\left(3a+1\right)$$

Solution Steps

Factor out 6.

$$6\left(-a-3a^{2}\right)$$

Consider -a-3a^{2}. Factor out a.

$$a\left(-1-3a\right)$$

Rewrite the complete factored expression.

$$6a\left(-3a-1\right)$$

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.

$$-18a^{2}-6a=0$$

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.

$$a=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\left(-18\right)}$$

Take the square root of \left(-6\right)^{2}.

$$a=\frac{-\left(-6\right)±6}{2\left(-18\right)}$$

The opposite of -6 is 6.

$$a=\frac{6±6}{2\left(-18\right)}$$

Multiply 2 times -18.

$$a=\frac{6±6}{-36}$$

Now solve the equation a=\frac{6±6}{-36} when ± is plus. Add 6 to 6.

$$a=\frac{12}{-36}$$

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

$$a=-\frac{1}{3}$$

Now solve the equation a=\frac{6±6}{-36} when ± is minus. Subtract 6 from 6.

$$a=\frac{0}{-36}$$

Divide 0 by -36.

$$a=0$$

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

$$-18a^{2}-6a=-18\left(a-\left(-\frac{1}{3}\right)\right)a$$

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

$$-18a^{2}-6a=-18\left(a+\frac{1}{3}\right)a$$

Add \frac{1}{3} to a by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$-18a^{2}-6a=-18\times \frac{-3a-1}{-3}a$$

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

$$-18a^{2}-6a=6\left(-3a-1\right)a$$

Evaluate

$$-6a\left(3a+1\right)$$