(6x-5)(6x-7)=0

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Solution for (6x-5)(6x-7)=0 equation: 


Simplifying
(6x + -5)(6x + -7) = 0

Reorder the terms:
(-5 + 6x)(6x + -7) = 0

Reorder the terms:
(-5 + 6x)(-7 + 6x) = 0

Multiply (-5 + 6x) * (-7 + 6x)
(-5(-7 + 6x) + 6x * (-7 + 6x)) = 0
((-7 * -5 + 6x * -5) + 6x * (-7 + 6x)) = 0
((35 + -30x) + 6x * (-7 + 6x)) = 0
(35 + -30x + (-7 * 6x + 6x * 6x)) = 0
(35 + -30x + (-42x + 36x2)) = 0

Combine like terms: -30x + -42x = -72x
(35 + -72x + 36x2) = 0

Solving
35 + -72x + 36x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -6x)(7 + -6x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {0.8333333333, 1.166666667}

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