(6x+5)(6x+5)-25=0

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Solution for (6x+5)(6x+5)-25=0 equation: 


Simplifying
(6x + 5)(6x + 5) + -25 = 0

Reorder the terms:
(5 + 6x)(6x + 5) + -25 = 0

Reorder the terms:
(5 + 6x)(5 + 6x) + -25 = 0

Multiply (5 + 6x) * (5 + 6x)
(5(5 + 6x) + 6x * (5 + 6x)) + -25 = 0
((5 * 5 + 6x * 5) + 6x * (5 + 6x)) + -25 = 0
((25 + 30x) + 6x * (5 + 6x)) + -25 = 0
(25 + 30x + (5 * 6x + 6x * 6x)) + -25 = 0
(25 + 30x + (30x + 36x2)) + -25 = 0

Combine like terms: 30x + 30x = 60x
(25 + 60x + 36x2) + -25 = 0

Reorder the terms:
25 + -25 + 60x + 36x2 = 0

Combine like terms: 25 + -25 = 0
0 + 60x + 36x2 = 0
60x + 36x2 = 0

Solving
60x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(5 + 3x) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {0, -1.666666667}

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