9x(x+5)=x-32

Solution for 9x(x+5)=x-32 equation:

Simplifying
9x(x + 5) = x + -32

Reorder the terms:
9x(5 + x) = x + -32
(5 * 9x + x * 9x) = x + -32
(45x + 9x2) = x + -32

Reorder the terms:
45x + 9x2 = -32 + x

Solving
45x + 9x2 = -32 + x

Solving for variable 'x'.

Reorder the terms:
32 + 45x + -1x + 9x2 = -32 + x + 32 + -1x

Combine like terms: 45x + -1x = 44x
32 + 44x + 9x2 = -32 + x + 32 + -1x

Reorder the terms:
32 + 44x + 9x2 = -32 + 32 + x + -1x

Combine like terms: -32 + 32 = 0
32 + 44x + 9x2 = 0 + x + -1x
32 + 44x + 9x2 = x + -1x

Combine like terms: x + -1x = 0
32 + 44x + 9x2 = 0

Factor a trinomial.
(4 + x)(8 + 9x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(8 + 9x)' equal to zero and attempt to solve:

Simplifying
8 + 9x = 0

Solving
8 + 9x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 9x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 9x = 0 + -8
9x = 0 + -8

Combine like terms: 0 + -8 = -8
9x = -8

Divide each side by '9'.
x = -0.8888888889

Simplifying
x = -0.8888888889
Solution
x = {-4, -0.8888888889}