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

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


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

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

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

Multiply (7 + -6x) * (-5 + 7x)
(7(-5 + 7x) + -6x * (-5 + 7x)) = 0
((-5 * 7 + 7x * 7) + -6x * (-5 + 7x)) = 0
((-35 + 49x) + -6x * (-5 + 7x)) = 0
(-35 + 49x + (-5 * -6x + 7x * -6x)) = 0
(-35 + 49x + (30x + -42x2)) = 0

Combine like terms: 49x + 30x = 79x
(-35 + 79x + -42x2) = 0

Solving
-35 + 79x + -42x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -7x)' equal to zero and attempt to solve:

Simplifying
5 + -7x = 0

Solving
5 + -7x = 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 + -7x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7x = 0 + -5
-7x = 0 + -5

Combine like terms: 0 + -5 = -5
-7x = -5

Divide each side by '-7'.
x = 0.7142857143

Simplifying
x = 0.7142857143
Solution
x = {1.166666667, 0.7142857143}

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