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

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


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

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

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

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

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

Add '-25' to each side of the equation.
25 + -60x + -25 + 36x2 = 25 + -25

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

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

Combine like terms: 25 + -25 = 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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