(2x+5)*(2x+5)-(2x+5)-6=0

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Solution for (2x+5)*(2x+5)-(2x+5)-6=0 equation: 


Simplifying
(2x + 5)(2x + 5) + -1(2x + 5) + -6 = 0

Reorder the terms:
(5 + 2x)(2x + 5) + -1(2x + 5) + -6 = 0

Reorder the terms:
(5 + 2x)(5 + 2x) + -1(2x + 5) + -6 = 0

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) + -1(2x + 5) + -6 = 0
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) + -1(2x + 5) + -6 = 0
((25 + 10x) + 2x * (5 + 2x)) + -1(2x + 5) + -6 = 0
(25 + 10x + (5 * 2x + 2x * 2x)) + -1(2x + 5) + -6 = 0
(25 + 10x + (10x + 4x2)) + -1(2x + 5) + -6 = 0

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) + -1(2x + 5) + -6 = 0

Reorder the terms:
25 + 20x + 4x2 + -1(5 + 2x) + -6 = 0
25 + 20x + 4x2 + (5 * -1 + 2x * -1) + -6 = 0
25 + 20x + 4x2 + (-5 + -2x) + -6 = 0

Reorder the terms:
25 + -5 + -6 + 20x + -2x + 4x2 = 0

Combine like terms: 25 + -5 = 20
20 + -6 + 20x + -2x + 4x2 = 0

Combine like terms: 20 + -6 = 14
14 + 20x + -2x + 4x2 = 0

Combine like terms: 20x + -2x = 18x
14 + 18x + 4x2 = 0

Solving
14 + 18x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 9x + 2x2) = 0

Factor a trinomial.
2((7 + 2x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, -1}

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