Solve -9x^2-15x

$$- 9 x ^ { 2 } - 15 x$$

Factor

$$-3x\left(3x+5\right)$$

Solution Steps

Factor out 3.

$$3\left(-3x^{2}-5x\right)$$

Consider -3x^{2}-5x. Factor out x.

$$x\left(-3x-5\right)$$

Rewrite the complete factored expression.

$$3x\left(-3x-5\right)$$

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.

$$-9x^{2}-15x=0$$

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.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2\left(-9\right)}$$

Take the square root of \left(-15\right)^{2}.

$$x=\frac{-\left(-15\right)±15}{2\left(-9\right)}$$

The opposite of -15 is 15.

$$x=\frac{15±15}{2\left(-9\right)}$$

Multiply 2 times -9.

$$x=\frac{15±15}{-18}$$

Now solve the equation x=\frac{15±15}{-18} when ± is plus. Add 15 to 15.

$$x=\frac{30}{-18}$$

Reduce the fraction \frac{30}{-18} to lowest terms by extracting and canceling out 6.

$$x=-\frac{5}{3}$$

Now solve the equation x=\frac{15±15}{-18} when ± is minus. Subtract 15 from 15.

$$x=\frac{0}{-18}$$

Divide 0 by -18.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\frac{5}{3} for x_{1} and 0 for x_{2}.

$$-9x^{2}-15x=-9\left(x-\left(-\frac{5}{3}\right)\right)x$$

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

$$-9x^{2}-15x=-9\left(x+\frac{5}{3}\right)x$$

Add \frac{5}{3} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$-9x^{2}-15x=-9\times \frac{-3x-5}{-3}x$$

Cancel out 3, the greatest common factor in -9 and -3.

$$-9x^{2}-15x=3\left(-3x-5\right)x$$

Evaluate

$$-3x\left(3x+5\right)$$