(2x+3)(2x+3)=1

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Solution for (2x+3)(2x+3)=1 equation: 


Simplifying
(2x + 3)(2x + 3) = 1

Reorder the terms:
(3 + 2x)(2x + 3) = 1

Reorder the terms:
(3 + 2x)(3 + 2x) = 1

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) = 1
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 1
((9 + 6x) + 2x * (3 + 2x)) = 1
(9 + 6x + (3 * 2x + 2x * 2x)) = 1
(9 + 6x + (6x + 4x2)) = 1

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) = 1

Solving
9 + 12x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
9 + -1 + 12x + 4x2 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + 12x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 3x + x2) = 0

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

Ignore the factor 4.

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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