(6x-4)(7x-5)=0

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Solution for (6x-4)(7x-5)=0 equation: 


Simplifying
(6x + -4)(7x + -5) = 0

Reorder the terms:
(-4 + 6x)(7x + -5) = 0

Reorder the terms:
(-4 + 6x)(-5 + 7x) = 0

Multiply (-4 + 6x) * (-5 + 7x)
(-4(-5 + 7x) + 6x * (-5 + 7x)) = 0
((-5 * -4 + 7x * -4) + 6x * (-5 + 7x)) = 0
((20 + -28x) + 6x * (-5 + 7x)) = 0
(20 + -28x + (-5 * 6x + 7x * 6x)) = 0
(20 + -28x + (-30x + 42x2)) = 0

Combine like terms: -28x + -30x = -58x
(20 + -58x + 42x2) = 0

Solving
20 + -58x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -29x + 21x2) = 0

Factor a trinomial.
2((2 + -3x)(5 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

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 = {0.6666666667, 0.7142857143}

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