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

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


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

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

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

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

Combine like terms: -42x + 32x = -10x
(-48 + -10x + 28x2) = 0

Solving
-48 + -10x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -5x + 14x2) = 0

Factor a trinomial.
2((-8 + -7x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.142857143, 1.5}

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