9x+81=(x+5)(x+5)

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Solution for 9x+81=(x+5)(x+5) equation: 


Simplifying
9x + 81 = (x + 5)(x + 5)

Reorder the terms:
81 + 9x = (x + 5)(x + 5)

Reorder the terms:
81 + 9x = (5 + x)(x + 5)

Reorder the terms:
81 + 9x = (5 + x)(5 + x)

Multiply (5 + x) * (5 + x)
81 + 9x = (5(5 + x) + x(5 + x))
81 + 9x = ((5 * 5 + x * 5) + x(5 + x))
81 + 9x = ((25 + 5x) + x(5 + x))
81 + 9x = (25 + 5x + (5 * x + x * x))
81 + 9x = (25 + 5x + (5x + x2))

Combine like terms: 5x + 5x = 10x
81 + 9x = (25 + 10x + x2)

Solving
81 + 9x = 25 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
81 + -25 + 9x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 81 + -25 = 56
56 + 9x + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Combine like terms: 9x + -10x = -1x
56 + -1x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2

Reorder the terms:
56 + -1x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
56 + -1x + -1x2 = 0 + 10x + -10x + x2 + -1x2
56 + -1x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
56 + -1x + -1x2 = 0 + x2 + -1x2
56 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
56 + -1x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(8 + x) = 0


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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {7, -8}

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