(2x+1)(2x+1)=81

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Solution for (2x+1)(2x+1)=81 equation: 


Simplifying
(2x + 1)(2x + 1) = 81

Reorder the terms:
(1 + 2x)(2x + 1) = 81

Reorder the terms:
(1 + 2x)(1 + 2x) = 81

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = 81
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 81
((1 + 2x) + 2x * (1 + 2x)) = 81
(1 + 2x + (1 * 2x + 2x * 2x)) = 81
(1 + 2x + (2x + 4x2)) = 81

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) = 81

Solving
1 + 4x + 4x2 = 81

Solving for variable 'x'.

Reorder the terms:
1 + -81 + 4x + 4x2 = 81 + -81

Combine like terms: 1 + -81 = -80
-80 + 4x + 4x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-80 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-20 + x + x2) = 0

Factor a trinomial.
4((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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