Solve 15x^2+8x

$$15 x ^ { 2 } + 8 x$$

Factor

$$x\left(15x+8\right)$$

Solution Steps

Factor out x.

$$x\left(15x+8\right)$$

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.

$$15x^{2}+8x=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}}}{2\times 15}$$

Take the square root of 8^{2}.

$$x=\frac{-8±8}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{-8±8}{30}$$

Now solve the equation x=\frac{-8±8}{30} when ± is plus. Add -8 to 8.

$$x=\frac{0}{30}$$

Divide 0 by 30.

$$x=0$$

Now solve the equation x=\frac{-8±8}{30} when ± is minus. Subtract 8 from -8.

$$x=-\frac{16}{30}$$

Reduce the fraction \frac{-16}{30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{8}{15}$$

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{8}{15} for x_{2}.

$$15x^{2}+8x=15x\left(x-\left(-\frac{8}{15}\right)\right)$$

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

$$15x^{2}+8x=15x\left(x+\frac{8}{15}\right)$$

Add \frac{8}{15} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$15x^{2}+8x=15x\times \frac{15x+8}{15}$$

Cancel out 15, the greatest common factor in 15 and 15.

$$15x^{2}+8x=x\left(15x+8\right)$$

Evaluate

$$x\left(15x+8\right)$$