(2x+5)(2x+5)=1

Solution for (2x+5)(2x+5)=1 equation:

Simplifying
(2x + 5)(2x + 5) = 1

Reorder the terms:
(5 + 2x)(2x + 5) = 1

Reorder the terms:
(5 + 2x)(5 + 2x) = 1

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) = 1
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 1
((25 + 10x) + 2x * (5 + 2x)) = 1
(25 + 10x + (5 * 2x + 2x * 2x)) = 1
(25 + 10x + (10x + 4x2)) = 1

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) = 1

Solving
25 + 20x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
25 + -1 + 20x + 4x2 = 1 + -1

Combine like terms: 25 + -1 = 24
24 + 20x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
24 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 5x + x2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Subproblem 2
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
Solution
x = {-3, -2}