(2x+1)(2x+1)-9=0

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Solution for (2x+1)(2x+1)-9=0 equation: 


Simplifying
(2x + 1)(2x + 1) + -9 = 0

Reorder the terms:
(1 + 2x)(2x + 1) + -9 = 0

Reorder the terms:
(1 + 2x)(1 + 2x) + -9 = 0

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) + -9 = 0
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -9 = 0
((1 + 2x) + 2x * (1 + 2x)) + -9 = 0
(1 + 2x + (1 * 2x + 2x * 2x)) + -9 = 0
(1 + 2x + (2x + 4x2)) + -9 = 0

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) + -9 = 0

Reorder the terms:
1 + -9 + 4x + 4x2 = 0

Combine like terms: 1 + -9 = -8
-8 + 4x + 4x2 = 0

Solving
-8 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + x + x2) = 0

Factor a trinomial.
4((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1}

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