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

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Solution for (13-x^2)=(x+1)(x+1) equation: 


Simplifying
(13 + -1x2) = (x + 1)(x + 1)

Remove parenthesis around (13 + -1x2)
13 + -1x2 = (x + 1)(x + 1)

Reorder the terms:
13 + -1x2 = (1 + x)(x + 1)

Reorder the terms:
13 + -1x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
13 + -1x2 = (1(1 + x) + x(1 + x))
13 + -1x2 = ((1 * 1 + x * 1) + x(1 + x))
13 + -1x2 = ((1 + 1x) + x(1 + x))
13 + -1x2 = (1 + 1x + (1 * x + x * x))
13 + -1x2 = (1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
13 + -1x2 = (1 + 2x + x2)

Solving
13 + -1x2 = 1 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
13 + -1 + -2x + -1x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 13 + -1 = 12
12 + -2x + -1x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
12 + -2x + -2x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
12 + -2x + -2x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
12 + -2x + -2x2 = 0 + 2x + -2x + x2 + -1x2
12 + -2x + -2x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
12 + -2x + -2x2 = 0 + x2 + -1x2
12 + -2x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -1x + -1x2) = 0

Factor a trinomial.
2((2 + -1x)(3 + x)) = 0

Ignore the factor 2.

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {2, -3}

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