x(x)+(x+8)(x+8)=(x+16)(x+16)

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Solution for x(x)+(x+8)(x+8)=(x+16)(x+16) equation: 


Simplifying
x(x) + (x + 8)(x + 8) = (x + 16)(x + 16)

Multiply x * x
x2 + (x + 8)(x + 8) = (x + 16)(x + 16)

Reorder the terms:
x2 + (8 + x)(x + 8) = (x + 16)(x + 16)

Reorder the terms:
x2 + (8 + x)(8 + x) = (x + 16)(x + 16)

Multiply (8 + x) * (8 + x)
x2 + (8(8 + x) + x(8 + x)) = (x + 16)(x + 16)
x2 + ((8 * 8 + x * 8) + x(8 + x)) = (x + 16)(x + 16)
x2 + ((64 + 8x) + x(8 + x)) = (x + 16)(x + 16)
x2 + (64 + 8x + (8 * x + x * x)) = (x + 16)(x + 16)
x2 + (64 + 8x + (8x + x2)) = (x + 16)(x + 16)

Combine like terms: 8x + 8x = 16x
x2 + (64 + 16x + x2) = (x + 16)(x + 16)

Reorder the terms:
64 + 16x + x2 + x2 = (x + 16)(x + 16)

Combine like terms: x2 + x2 = 2x2
64 + 16x + 2x2 = (x + 16)(x + 16)

Reorder the terms:
64 + 16x + 2x2 = (16 + x)(x + 16)

Reorder the terms:
64 + 16x + 2x2 = (16 + x)(16 + x)

Multiply (16 + x) * (16 + x)
64 + 16x + 2x2 = (16(16 + x) + x(16 + x))
64 + 16x + 2x2 = ((16 * 16 + x * 16) + x(16 + x))
64 + 16x + 2x2 = ((256 + 16x) + x(16 + x))
64 + 16x + 2x2 = (256 + 16x + (16 * x + x * x))
64 + 16x + 2x2 = (256 + 16x + (16x + x2))

Combine like terms: 16x + 16x = 32x
64 + 16x + 2x2 = (256 + 32x + x2)

Solving
64 + 16x + 2x2 = 256 + 32x + x2

Solving for variable 'x'.

Reorder the terms:
64 + -256 + 16x + -32x + 2x2 + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2

Combine like terms: 64 + -256 = -192
-192 + 16x + -32x + 2x2 + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2

Combine like terms: 16x + -32x = -16x
-192 + -16x + 2x2 + -1x2 = 256 + 32x + x2 + -256 + -32x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-192 + -16x + 1x2 = 256 + 32x + x2 + -256 + -32x + -1x2

Reorder the terms:
-192 + -16x + 1x2 = 256 + -256 + 32x + -32x + x2 + -1x2

Combine like terms: 256 + -256 = 0
-192 + -16x + 1x2 = 0 + 32x + -32x + x2 + -1x2
-192 + -16x + 1x2 = 32x + -32x + x2 + -1x2

Combine like terms: 32x + -32x = 0
-192 + -16x + 1x2 = 0 + x2 + -1x2
-192 + -16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-192 + -16x + 1x2 = 0

Factor a trinomial.
(-8 + -1x)(24 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1x = 0 + -24
-1x = 0 + -24

Combine like terms: 0 + -24 = -24
-1x = -24

Divide each side by '-1'.
x = 24

Simplifying
x = 24
Solution
x = {-8, 24}

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