(7x-8)(6x+4)=0

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Solution for (7x-8)(6x+4)=0 equation: 


Simplifying
(7x + -8)(6x + 4) = 0

Reorder the terms:
(-8 + 7x)(6x + 4) = 0

Reorder the terms:
(-8 + 7x)(4 + 6x) = 0

Multiply (-8 + 7x) * (4 + 6x)
(-8(4 + 6x) + 7x * (4 + 6x)) = 0
((4 * -8 + 6x * -8) + 7x * (4 + 6x)) = 0
((-32 + -48x) + 7x * (4 + 6x)) = 0
(-32 + -48x + (4 * 7x + 6x * 7x)) = 0
(-32 + -48x + (28x + 42x2)) = 0

Combine like terms: -48x + 28x = -20x
(-32 + -20x + 42x2) = 0

Solving
-32 + -20x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -10x + 21x2) = 0

Factor a trinomial.
2((-2 + -3x)(8 + -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 '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

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

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

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {-0.6666666667, 1.142857143}

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