Solve -18x^2-27x

$$-18 { x }^{ 2 } -27x$$

Factor

$$-9x\left(2x+3\right)$$

Solution Steps

Factor out 9.

$$9\left(-2x^{2}-3x\right)$$

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

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

Rewrite the complete factored expression.

$$9x\left(-2x-3\right)$$

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.

$$-18x^{2}-27x=0$$

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.

$$x=\frac{-\left(-27\right)±\sqrt{\left(-27\right)^{2}}}{2\left(-18\right)}$$

Take the square root of \left(-27\right)^{2}.

$$x=\frac{-\left(-27\right)±27}{2\left(-18\right)}$$

The opposite of -27 is 27.

$$x=\frac{27±27}{2\left(-18\right)}$$

Multiply 2 times -18.

$$x=\frac{27±27}{-36}$$

Now solve the equation x=\frac{27±27}{-36} when ± is plus. Add 27 to 27.

$$x=\frac{54}{-36}$$

Reduce the fraction \frac{54}{-36} to lowest terms by extracting and canceling out 18.

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

Now solve the equation x=\frac{27±27}{-36} when ± is minus. Subtract 27 from 27.

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

Divide 0 by -36.

$$x=0$$

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

$$-18x^{2}-27x=-18\left(x-\left(-\frac{3}{2}\right)\right)x$$

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

$$-18x^{2}-27x=-18\left(x+\frac{3}{2}\right)x$$

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

$$-18x^{2}-27x=-18\times \frac{-2x-3}{-2}x$$

Cancel out 2, the greatest common factor in -18 and -2.

$$-18x^{2}-27x=9\left(-2x-3\right)x$$

Evaluate

$$-9x\left(2x+3\right)$$