(6x-7)(8x-8)=0

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Solution for (6x-7)(8x-8)=0 equation: 


Simplifying
(6x + -7)(8x + -8) = 0

Reorder the terms:
(-7 + 6x)(8x + -8) = 0

Reorder the terms:
(-7 + 6x)(-8 + 8x) = 0

Multiply (-7 + 6x) * (-8 + 8x)
(-7(-8 + 8x) + 6x * (-8 + 8x)) = 0
((-8 * -7 + 8x * -7) + 6x * (-8 + 8x)) = 0
((56 + -56x) + 6x * (-8 + 8x)) = 0
(56 + -56x + (-8 * 6x + 8x * 6x)) = 0
(56 + -56x + (-48x + 48x2)) = 0

Combine like terms: -56x + -48x = -104x
(56 + -104x + 48x2) = 0

Solving
56 + -104x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(7 + -13x + 6x2) = 0

Factor a trinomial.
8((1 + -1x)(7 + -6x)) = 0

Ignore the factor 8.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

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 = {1, 1.166666667}

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