8x(x+3)-15(x-3)=90

Solution for 8x(x+3)-15(x-3)=90 equation:

Simplifying
8x(x + 3) + -15(x + -3) = 90

Reorder the terms:
8x(3 + x) + -15(x + -3) = 90
(3 * 8x + x * 8x) + -15(x + -3) = 90
(24x + 8x2) + -15(x + -3) = 90

Reorder the terms:
24x + 8x2 + -15(-3 + x) = 90
24x + 8x2 + (-3 * -15 + x * -15) = 90
24x + 8x2 + (45 + -15x) = 90

Reorder the terms:
45 + 24x + -15x + 8x2 = 90

Combine like terms: 24x + -15x = 9x
45 + 9x + 8x2 = 90

Solving
45 + 9x + 8x2 = 90

Solving for variable 'x'.

Reorder the terms:
45 + -90 + 9x + 8x2 = 90 + -90

Combine like terms: 45 + -90 = -45
-45 + 9x + 8x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-45 + 9x + 8x2 = 0

Factor a trinomial.
(-3 + -1x)(15 + -8x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(15 + -8x)' equal to zero and attempt to solve:

Simplifying
15 + -8x = 0

Solving
15 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + -8x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -8x = 0 + -15
-8x = 0 + -15

Combine like terms: 0 + -15 = -15
-8x = -15

Divide each side by '-8'.
x = 1.875

Simplifying
x = 1.875
Solution
x = {-3, 1.875}