(2x+1)(2x+1)=25

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Solution for (2x+1)(2x+1)=25 equation: 


Simplifying
(2x + 1)(2x + 1) = 25

Reorder the terms:
(1 + 2x)(2x + 1) = 25

Reorder the terms:
(1 + 2x)(1 + 2x) = 25

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = 25
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 25
((1 + 2x) + 2x * (1 + 2x)) = 25
(1 + 2x + (1 * 2x + 2x * 2x)) = 25
(1 + 2x + (2x + 4x2)) = 25

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) = 25

Solving
1 + 4x + 4x2 = 25

Solving for variable 'x'.

Reorder the terms:
1 + -25 + 4x + 4x2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 4x + 4x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 2}

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