(2x+5)(2x+5)+(2x+5)=0

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Solution for (2x+5)(2x+5)+(2x+5)=0 equation: 


Simplifying
(2x + 5)(2x + 5) + (2x + 5) = 0

Reorder the terms:
(5 + 2x)(2x + 5) + (2x + 5) = 0

Reorder the terms:
(5 + 2x)(5 + 2x) + (2x + 5) = 0

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) + (2x + 5) = 0
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) + (2x + 5) = 0
((25 + 10x) + 2x * (5 + 2x)) + (2x + 5) = 0
(25 + 10x + (5 * 2x + 2x * 2x)) + (2x + 5) = 0
(25 + 10x + (10x + 4x2)) + (2x + 5) = 0

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) + (2x + 5) = 0

Reorder the terms:
25 + 20x + 4x2 + (5 + 2x) = 0

Remove parenthesis around (5 + 2x)
25 + 20x + 4x2 + 5 + 2x = 0

Reorder the terms:
25 + 5 + 20x + 2x + 4x2 = 0

Combine like terms: 25 + 5 = 30
30 + 20x + 2x + 4x2 = 0

Combine like terms: 20x + 2x = 22x
30 + 22x + 4x2 = 0

Solving
30 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 11x + 2x2) = 0

Factor a trinomial.
2((3 + x)(5 + 2x)) = 0

Ignore the factor 2.

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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {-3, -2.5}

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