2x+15=(x+6)(x+6)

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Solution for 2x+15=(x+6)(x+6) equation: 


Simplifying
2x + 15 = (x + 6)(x + 6)

Reorder the terms:
15 + 2x = (x + 6)(x + 6)

Reorder the terms:
15 + 2x = (6 + x)(x + 6)

Reorder the terms:
15 + 2x = (6 + x)(6 + x)

Multiply (6 + x) * (6 + x)
15 + 2x = (6(6 + x) + x(6 + x))
15 + 2x = ((6 * 6 + x * 6) + x(6 + x))
15 + 2x = ((36 + 6x) + x(6 + x))
15 + 2x = (36 + 6x + (6 * x + x * x))
15 + 2x = (36 + 6x + (6x + x2))

Combine like terms: 6x + 6x = 12x
15 + 2x = (36 + 12x + x2)

Solving
15 + 2x = 36 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
15 + -36 + 2x + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 15 + -36 = -21
-21 + 2x + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 2x + -12x = -10x
-21 + -10x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Reorder the terms:
-21 + -10x + -1x2 = 36 + -36 + 12x + -12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-21 + -10x + -1x2 = 0 + 12x + -12x + x2 + -1x2
-21 + -10x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-21 + -10x + -1x2 = 0 + x2 + -1x2
-21 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + -10x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 10x + x2) = 0

Factor a trinomial.
-1((7 + x)(3 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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 = {-7, -3}

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