2x+19=(x+8)(x+8)

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Solution for 2x+19=(x+8)(x+8) equation: 


Simplifying
2x + 19 = (x + 8)(x + 8)

Reorder the terms:
19 + 2x = (x + 8)(x + 8)

Reorder the terms:
19 + 2x = (8 + x)(x + 8)

Reorder the terms:
19 + 2x = (8 + x)(8 + x)

Multiply (8 + x) * (8 + x)
19 + 2x = (8(8 + x) + x(8 + x))
19 + 2x = ((8 * 8 + x * 8) + x(8 + x))
19 + 2x = ((64 + 8x) + x(8 + x))
19 + 2x = (64 + 8x + (8 * x + x * x))
19 + 2x = (64 + 8x + (8x + x2))

Combine like terms: 8x + 8x = 16x
19 + 2x = (64 + 16x + x2)

Solving
19 + 2x = 64 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
19 + -64 + 2x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 19 + -64 = -45
-45 + 2x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 2x + -16x = -14x
-45 + -14x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Reorder the terms:
-45 + -14x + -1x2 = 64 + -64 + 16x + -16x + x2 + -1x2

Combine like terms: 64 + -64 = 0
-45 + -14x + -1x2 = 0 + 16x + -16x + x2 + -1x2
-45 + -14x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-45 + -14x + -1x2 = 0 + x2 + -1x2
-45 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-45 + -14x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(45 + 14x + x2) = 0

Factor a trinomial.
-1((9 + x)(5 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-9, -5}

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