2x+13=(x+5)(x+5)

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Solution for 2x+13=(x+5)(x+5) equation: 


Simplifying
2x + 13 = (x + 5)(x + 5)

Reorder the terms:
13 + 2x = (x + 5)(x + 5)

Reorder the terms:
13 + 2x = (5 + x)(x + 5)

Reorder the terms:
13 + 2x = (5 + x)(5 + x)

Multiply (5 + x) * (5 + x)
13 + 2x = (5(5 + x) + x(5 + x))
13 + 2x = ((5 * 5 + x * 5) + x(5 + x))
13 + 2x = ((25 + 5x) + x(5 + x))
13 + 2x = (25 + 5x + (5 * x + x * x))
13 + 2x = (25 + 5x + (5x + x2))

Combine like terms: 5x + 5x = 10x
13 + 2x = (25 + 10x + x2)

Solving
13 + 2x = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
13 + -25 + 2x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 13 + -25 = -12
-12 + 2x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 2x + -10x = -8x
-12 + -8x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
-12 + -8x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-12 + -8x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-12 + -8x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-12 + -8x + -1x2 = 0 + x2 + -1x2
-12 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 8x + x2) = 0

Factor a trinomial.
-1((6 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-6, -2}

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