x^2+((x+7)(x+7))=((x+8)(x+8))

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Solution for x^2+((x+7)(x+7))=((x+8)(x+8)) equation: 


Simplifying
x2 + ((x + 7)(x + 7)) = ((x + 8)(x + 8))

Reorder the terms:
x2 + ((7 + x)(x + 7)) = ((x + 8)(x + 8))

Reorder the terms:
x2 + ((7 + x)(7 + x)) = ((x + 8)(x + 8))

Multiply (7 + x) * (7 + x)
x2 + ((7(7 + x) + x(7 + x))) = ((x + 8)(x + 8))
x2 + (((7 * 7 + x * 7) + x(7 + x))) = ((x + 8)(x + 8))
x2 + (((49 + 7x) + x(7 + x))) = ((x + 8)(x + 8))
x2 + ((49 + 7x + (7 * x + x * x))) = ((x + 8)(x + 8))
x2 + ((49 + 7x + (7x + x2))) = ((x + 8)(x + 8))

Combine like terms: 7x + 7x = 14x
x2 + ((49 + 14x + x2)) = ((x + 8)(x + 8))
x2 + (49 + 14x + x2) = ((x + 8)(x + 8))

Remove parenthesis around (49 + 14x + x2)
x2 + 49 + 14x + x2 = ((x + 8)(x + 8))

Reorder the terms:
49 + 14x + x2 + x2 = ((x + 8)(x + 8))

Combine like terms: x2 + x2 = 2x2
49 + 14x + 2x2 = ((x + 8)(x + 8))

Reorder the terms:
49 + 14x + 2x2 = ((8 + x)(x + 8))

Reorder the terms:
49 + 14x + 2x2 = ((8 + x)(8 + x))

Multiply (8 + x) * (8 + x)
49 + 14x + 2x2 = ((8(8 + x) + x(8 + x)))
49 + 14x + 2x2 = (((8 * 8 + x * 8) + x(8 + x)))
49 + 14x + 2x2 = (((64 + 8x) + x(8 + x)))
49 + 14x + 2x2 = ((64 + 8x + (8 * x + x * x)))
49 + 14x + 2x2 = ((64 + 8x + (8x + x2)))

Combine like terms: 8x + 8x = 16x
49 + 14x + 2x2 = ((64 + 16x + x2))
49 + 14x + 2x2 = (64 + 16x + x2)

Remove parenthesis around (64 + 16x + x2)
49 + 14x + 2x2 = 64 + 16x + x2

Solving
49 + 14x + 2x2 = 64 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
49 + -64 + 14x + -16x + 2x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 49 + -64 = -15
-15 + 14x + -16x + 2x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 14x + -16x = -2x
-15 + -2x + 2x2 + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-15 + -2x + 1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Reorder the terms:
-15 + -2x + 1x2 = 64 + -64 + 16x + -16x + x2 + -1x2

Combine like terms: 64 + -64 = 0
-15 + -2x + 1x2 = 0 + 16x + -16x + x2 + -1x2
-15 + -2x + 1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-15 + -2x + 1x2 = 0 + x2 + -1x2
-15 + -2x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + -2x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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