(5x-5)(8x-7)=0

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Solution for (5x-5)(8x-7)=0 equation: 


Simplifying
(5x + -5)(8x + -7) = 0

Reorder the terms:
(-5 + 5x)(8x + -7) = 0

Reorder the terms:
(-5 + 5x)(-7 + 8x) = 0

Multiply (-5 + 5x) * (-7 + 8x)
(-5(-7 + 8x) + 5x * (-7 + 8x)) = 0
((-7 * -5 + 8x * -5) + 5x * (-7 + 8x)) = 0
((35 + -40x) + 5x * (-7 + 8x)) = 0
(35 + -40x + (-7 * 5x + 8x * 5x)) = 0
(35 + -40x + (-35x + 40x2)) = 0

Combine like terms: -40x + -35x = -75x
(35 + -75x + 40x2) = 0

Solving
35 + -75x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + -15x + 8x2) = 0

Factor a trinomial.
5((7 + -8x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 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 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875

Subproblem 2
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
Solution
x = {0.875, 1}

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