(2x+7)(2x+7)=81

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Solution for (2x+7)(2x+7)=81 equation: 


Simplifying
(2x + 7)(2x + 7) = 81

Reorder the terms:
(7 + 2x)(2x + 7) = 81

Reorder the terms:
(7 + 2x)(7 + 2x) = 81

Multiply (7 + 2x) * (7 + 2x)
(7(7 + 2x) + 2x * (7 + 2x)) = 81
((7 * 7 + 2x * 7) + 2x * (7 + 2x)) = 81
((49 + 14x) + 2x * (7 + 2x)) = 81
(49 + 14x + (7 * 2x + 2x * 2x)) = 81
(49 + 14x + (14x + 4x2)) = 81

Combine like terms: 14x + 14x = 28x
(49 + 28x + 4x2) = 81

Solving
49 + 28x + 4x2 = 81

Solving for variable 'x'.

Reorder the terms:
49 + -81 + 28x + 4x2 = 81 + -81

Combine like terms: 49 + -81 = -32
-32 + 28x + 4x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-32 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 7x + x2) = 0

Factor a trinomial.
4((-8 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-8, 1}

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