4(x-8)(x-8)+x^2=x(x+115)-43x

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Solution for 4(x-8)(x-8)+x^2=x(x+115)-43x equation: 


Simplifying
4(x + -8)(x + -8) + x2 = x(x + 115) + -43x

Reorder the terms:
4(-8 + x)(x + -8) + x2 = x(x + 115) + -43x

Reorder the terms:
4(-8 + x)(-8 + x) + x2 = x(x + 115) + -43x

Multiply (-8 + x) * (-8 + x)
4(-8(-8 + x) + x(-8 + x)) + x2 = x(x + 115) + -43x
4((-8 * -8 + x * -8) + x(-8 + x)) + x2 = x(x + 115) + -43x
4((64 + -8x) + x(-8 + x)) + x2 = x(x + 115) + -43x
4(64 + -8x + (-8 * x + x * x)) + x2 = x(x + 115) + -43x
4(64 + -8x + (-8x + x2)) + x2 = x(x + 115) + -43x

Combine like terms: -8x + -8x = -16x
4(64 + -16x + x2) + x2 = x(x + 115) + -43x
(64 * 4 + -16x * 4 + x2 * 4) + x2 = x(x + 115) + -43x
(256 + -64x + 4x2) + x2 = x(x + 115) + -43x

Combine like terms: 4x2 + x2 = 5x2
256 + -64x + 5x2 = x(x + 115) + -43x

Reorder the terms:
256 + -64x + 5x2 = x(115 + x) + -43x
256 + -64x + 5x2 = (115 * x + x * x) + -43x
256 + -64x + 5x2 = (115x + x2) + -43x

Reorder the terms:
256 + -64x + 5x2 = 115x + -43x + x2

Combine like terms: 115x + -43x = 72x
256 + -64x + 5x2 = 72x + x2

Solving
256 + -64x + 5x2 = 72x + x2

Solving for variable 'x'.

Reorder the terms:
256 + -64x + -72x + 5x2 + -1x2 = 72x + x2 + -72x + -1x2

Combine like terms: -64x + -72x = -136x
256 + -136x + 5x2 + -1x2 = 72x + x2 + -72x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
256 + -136x + 4x2 = 72x + x2 + -72x + -1x2

Reorder the terms:
256 + -136x + 4x2 = 72x + -72x + x2 + -1x2

Combine like terms: 72x + -72x = 0
256 + -136x + 4x2 = 0 + x2 + -1x2
256 + -136x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
256 + -136x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(64 + -34x + x2) = 0

Factor a trinomial.
4((2 + -1x)(32 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(32 + -1x)' equal to zero and attempt to solve:

Simplifying
32 + -1x = 0

Solving
32 + -1x = 0

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

Add '-32' to each side of the equation.
32 + -32 + -1x = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -1x = 0 + -32
-1x = 0 + -32

Combine like terms: 0 + -32 = -32
-1x = -32

Divide each side by '-1'.
x = 32

Simplifying
x = 32
Solution
x = {2, 32}

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