32(x^2+32x-150)=0

Solution for 32(x^2+32x-150)=0 equation:

Simplifying
32(x2 + 32x + -150) = 0

Reorder the terms:
32(-150 + 32x + x2) = 0
(-150 * 32 + 32x * 32 + x2 * 32) = 0
(-4800 + 1024x + 32x2) = 0

Solving
-4800 + 1024x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '32'.
32(-150 + 32x + x2) = 0

Ignore the factor 32.
Subproblem 1
Set the factor '(-150 + 32x + x2)' equal to zero and attempt to solve:

Simplifying
-150 + 32x + x2 = 0

Solving
-150 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + 32x + 150 + x2 = 0 + 150

Reorder the terms:
-150 + 150 + 32x + x2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 32x + x2 = 0 + 150
32x + x2 = 0 + 150

Combine like terms: 0 + 150 = 150
32x + x2 = 150

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = 150 + 256

Reorder the terms:
256 + 32x + x2 = 150 + 256

Combine like terms: 150 + 256 = 406
256 + 32x + x2 = 406

Factor a perfect square on the left side:
(x + 16)(x + 16) = 406

Calculate the square root of the right side: 20.14944168

Break this problem into two subproblems by setting 
(x + 16) equal to 20.14944168 and -20.14944168.

Subproblem 1
x + 16 = 20.14944168

Simplifying
x + 16 = 20.14944168

Reorder the terms:
16 + x = 20.14944168

Solving
16 + x = 20.14944168

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = 20.14944168 + -16

Combine like terms: 16 + -16 = 0
0 + x = 20.14944168 + -16
x = 20.14944168 + -16

Combine like terms: 20.14944168 + -16 = 4.14944168
x = 4.14944168

Simplifying
x = 4.14944168

Subproblem 2
x + 16 = -20.14944168

Simplifying
x + 16 = -20.14944168

Reorder the terms:
16 + x = -20.14944168

Solving
16 + x = -20.14944168

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = -20.14944168 + -16

Combine like terms: 16 + -16 = 0
0 + x = -20.14944168 + -16
x = -20.14944168 + -16

Combine like terms: -20.14944168 + -16 = -36.14944168
x = -36.14944168

Simplifying
x = -36.14944168

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.14944168, -36.14944168}
Solution
x = {4.14944168, -36.14944168}