(x+1)*(x+1)+x*x=(x+9)*(x+9)

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Solution for (x+1)*(x+1)+x*x=(x+9)*(x+9) equation: 


Simplifying
(x + 1)(x + 1) + x * x = (x + 9)(x + 9)

Reorder the terms:
(1 + x)(x + 1) + x * x = (x + 9)(x + 9)

Reorder the terms:
(1 + x)(1 + x) + x * x = (x + 9)(x + 9)

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) + x * x = (x + 9)(x + 9)
((1 * 1 + x * 1) + x(1 + x)) + x * x = (x + 9)(x + 9)
((1 + 1x) + x(1 + x)) + x * x = (x + 9)(x + 9)
(1 + 1x + (1 * x + x * x)) + x * x = (x + 9)(x + 9)
(1 + 1x + (1x + x2)) + x * x = (x + 9)(x + 9)

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + x * x = (x + 9)(x + 9)

Multiply x * x
1 + 2x + x2 + x2 = (x + 9)(x + 9)

Combine like terms: x2 + x2 = 2x2
1 + 2x + 2x2 = (x + 9)(x + 9)

Reorder the terms:
1 + 2x + 2x2 = (9 + x)(x + 9)

Reorder the terms:
1 + 2x + 2x2 = (9 + x)(9 + x)

Multiply (9 + x) * (9 + x)
1 + 2x + 2x2 = (9(9 + x) + x(9 + x))
1 + 2x + 2x2 = ((9 * 9 + x * 9) + x(9 + x))
1 + 2x + 2x2 = ((81 + 9x) + x(9 + x))
1 + 2x + 2x2 = (81 + 9x + (9 * x + x * x))
1 + 2x + 2x2 = (81 + 9x + (9x + x2))

Combine like terms: 9x + 9x = 18x
1 + 2x + 2x2 = (81 + 18x + x2)

Solving
1 + 2x + 2x2 = 81 + 18x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -81 + 2x + -18x + 2x2 + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2

Combine like terms: 1 + -81 = -80
-80 + 2x + -18x + 2x2 + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2

Combine like terms: 2x + -18x = -16x
-80 + -16x + 2x2 + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-80 + -16x + 1x2 = 81 + 18x + x2 + -81 + -18x + -1x2

Reorder the terms:
-80 + -16x + 1x2 = 81 + -81 + 18x + -18x + x2 + -1x2

Combine like terms: 81 + -81 = 0
-80 + -16x + 1x2 = 0 + 18x + -18x + x2 + -1x2
-80 + -16x + 1x2 = 18x + -18x + x2 + -1x2

Combine like terms: 18x + -18x = 0
-80 + -16x + 1x2 = 0 + x2 + -1x2
-80 + -16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-80 + -16x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(20 + -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 '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-4, 20}

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