-x^2+32=x^2-4x+16

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Solution for -x^2+32=x^2-4x+16 equation: 


Simplifying
-1x2 + 32 = x2 + -4x + 16

Reorder the terms:
32 + -1x2 = x2 + -4x + 16

Reorder the terms:
32 + -1x2 = 16 + -4x + x2

Solving
32 + -1x2 = 16 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
32 + -16 + 4x + -1x2 + -1x2 = 16 + -4x + x2 + -16 + 4x + -1x2

Combine like terms: 32 + -16 = 16
16 + 4x + -1x2 + -1x2 = 16 + -4x + x2 + -16 + 4x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
16 + 4x + -2x2 = 16 + -4x + x2 + -16 + 4x + -1x2

Reorder the terms:
16 + 4x + -2x2 = 16 + -16 + -4x + 4x + x2 + -1x2

Combine like terms: 16 + -16 = 0
16 + 4x + -2x2 = 0 + -4x + 4x + x2 + -1x2
16 + 4x + -2x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
16 + 4x + -2x2 = 0 + x2 + -1x2
16 + 4x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 2x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(2 + x)) = 0

Ignore the factor 2.

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {4, -2}

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