4x+(-32x+1)7=-7x+x^2-2(-12)

Solution for 4x+(-32x+1)7=-7x+x^2-2(-12) equation:

Simplifying
4x + (-32x + 1) * 7 = -7x + x2 + -2(-12)

Reorder the terms:
4x + (1 + -32x) * 7 = -7x + x2 + -2(-12)

Reorder the terms for easier multiplication:
4x + 7(1 + -32x) = -7x + x2 + -2(-12)
4x + (1 * 7 + -32x * 7) = -7x + x2 + -2(-12)
4x + (7 + -224x) = -7x + x2 + -2(-12)

Reorder the terms:
7 + 4x + -224x = -7x + x2 + -2(-12)

Combine like terms: 4x + -224x = -220x
7 + -220x = -7x + x2 + -2(-12)

Multiply -2 * -12
7 + -220x = -7x + x2 + 24

Reorder the terms:
7 + -220x = 24 + -7x + x2

Solving
7 + -220x = 24 + -7x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -24 + -220x + 7x + -1x2 = 24 + -7x + x2 + -24 + 7x + -1x2

Combine like terms: 7 + -24 = -17
-17 + -220x + 7x + -1x2 = 24 + -7x + x2 + -24 + 7x + -1x2

Combine like terms: -220x + 7x = -213x
-17 + -213x + -1x2 = 24 + -7x + x2 + -24 + 7x + -1x2

Reorder the terms:
-17 + -213x + -1x2 = 24 + -24 + -7x + 7x + x2 + -1x2

Combine like terms: 24 + -24 = 0
-17 + -213x + -1x2 = 0 + -7x + 7x + x2 + -1x2
-17 + -213x + -1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
-17 + -213x + -1x2 = 0 + x2 + -1x2
-17 + -213x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-17 + -213x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 213x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(17 + 213x + x2)' equal to zero and attempt to solve:

Simplifying
17 + 213x + x2 = 0

Solving
17 + 213x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 213x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 213x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 213x + x2 = 0 + -17
213x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
213x + x2 = -17

The x term is 213x.  Take half its coefficient (106.5).
Square it (11342.25) and add it to both sides.

Add '11342.25' to each side of the equation.
213x + 11342.25 + x2 = -17 + 11342.25

Reorder the terms:
11342.25 + 213x + x2 = -17 + 11342.25

Combine like terms: -17 + 11342.25 = 11325.25
11342.25 + 213x + x2 = 11325.25

Factor a perfect square on the left side:
(x + 106.5)(x + 106.5) = 11325.25

Calculate the square root of the right side: 106.420157865

Break this problem into two subproblems by setting 
(x + 106.5) equal to 106.420157865 and -106.420157865.

Subproblem 1
x + 106.5 = 106.420157865

Simplifying
x + 106.5 = 106.420157865

Reorder the terms:
106.5 + x = 106.420157865

Solving
106.5 + x = 106.420157865

Solving for variable 'x'.

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

Add '-106.5' to each side of the equation.
106.5 + -106.5 + x = 106.420157865 + -106.5

Combine like terms: 106.5 + -106.5 = 0.0
0.0 + x = 106.420157865 + -106.5
x = 106.420157865 + -106.5

Combine like terms: 106.420157865 + -106.5 = -0.079842135
x = -0.079842135

Simplifying
x = -0.079842135

Subproblem 2
x + 106.5 = -106.420157865

Simplifying
x + 106.5 = -106.420157865

Reorder the terms:
106.5 + x = -106.420157865

Solving
106.5 + x = -106.420157865

Solving for variable 'x'.

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

Add '-106.5' to each side of the equation.
106.5 + -106.5 + x = -106.420157865 + -106.5

Combine like terms: 106.5 + -106.5 = 0.0
0.0 + x = -106.420157865 + -106.5
x = -106.420157865 + -106.5

Combine like terms: -106.420157865 + -106.5 = -212.920157865
x = -212.920157865

Simplifying
x = -212.920157865

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.079842135, -212.920157865}
Solution
x = {-0.079842135, -212.920157865}