(2x+3)(2x+3)=25

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Solution for (2x+3)(2x+3)=25 equation: 


Simplifying
(2x + 3)(2x + 3) = 25

Reorder the terms:
(3 + 2x)(2x + 3) = 25

Reorder the terms:
(3 + 2x)(3 + 2x) = 25

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) = 25
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 25
((9 + 6x) + 2x * (3 + 2x)) = 25
(9 + 6x + (3 * 2x + 2x * 2x)) = 25
(9 + 6x + (6x + 4x2)) = 25

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) = 25

Solving
9 + 12x + 4x2 = 25

Solving for variable 'x'.

Reorder the terms:
9 + -25 + 12x + 4x2 = 25 + -25

Combine like terms: 9 + -25 = -16
-16 + 12x + 4x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-16 + 12x + 4x2 = 0

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

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

Ignore the factor 4.

Subproblem 1
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

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 = {-4, 1}

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