(7x-5)(6x+8)=0

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Solution for (7x-5)(6x+8)=0 equation: 


Simplifying
(7x + -5)(6x + 8) = 0

Reorder the terms:
(-5 + 7x)(6x + 8) = 0

Reorder the terms:
(-5 + 7x)(8 + 6x) = 0

Multiply (-5 + 7x) * (8 + 6x)
(-5(8 + 6x) + 7x * (8 + 6x)) = 0
((8 * -5 + 6x * -5) + 7x * (8 + 6x)) = 0
((-40 + -30x) + 7x * (8 + 6x)) = 0
(-40 + -30x + (8 * 7x + 6x * 7x)) = 0
(-40 + -30x + (56x + 42x2)) = 0

Combine like terms: -30x + 56x = 26x
(-40 + 26x + 42x2) = 0

Solving
-40 + 26x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 13x + 21x2) = 0

Factor a trinomial.
2((-4 + -3x)(5 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 0.7142857143}

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