(x-7)(x-7)+x^2=(x+1)(x+1)

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


Simplifying
(x + -7)(x + -7) + x2 = (x + 1)(x + 1)

Reorder the terms:
(-7 + x)(x + -7) + x2 = (x + 1)(x + 1)

Reorder the terms:
(-7 + x)(-7 + x) + x2 = (x + 1)(x + 1)

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) + x2 = (x + 1)(x + 1)
((-7 * -7 + x * -7) + x(-7 + x)) + x2 = (x + 1)(x + 1)
((49 + -7x) + x(-7 + x)) + x2 = (x + 1)(x + 1)
(49 + -7x + (-7 * x + x * x)) + x2 = (x + 1)(x + 1)
(49 + -7x + (-7x + x2)) + x2 = (x + 1)(x + 1)

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) + x2 = (x + 1)(x + 1)

Combine like terms: x2 + x2 = 2x2
49 + -14x + 2x2 = (x + 1)(x + 1)

Reorder the terms:
49 + -14x + 2x2 = (1 + x)(x + 1)

Reorder the terms:
49 + -14x + 2x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
49 + -14x + 2x2 = (1(1 + x) + x(1 + x))
49 + -14x + 2x2 = ((1 * 1 + x * 1) + x(1 + x))
49 + -14x + 2x2 = ((1 + 1x) + x(1 + x))
49 + -14x + 2x2 = (1 + 1x + (1 * x + x * x))
49 + -14x + 2x2 = (1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
49 + -14x + 2x2 = (1 + 2x + x2)

Solving
49 + -14x + 2x2 = 1 + 2x + x2

Solving for variable 'x'.

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

Combine like terms: 49 + -1 = 48
48 + -14x + -2x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: -14x + -2x = -16x
48 + -16x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
48 + -16x + 1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
48 + -16x + 1x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
48 + -16x + 1x2 = 0 + 2x + -2x + x2 + -1x2
48 + -16x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
48 + -16x + 1x2 = 0 + x2 + -1x2
48 + -16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + -16x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(12 + -1x) = 0


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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {4, 12}

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