(6x-5)(4x+8)=0

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Solution for (6x-5)(4x+8)=0 equation: 


Simplifying
(6x + -5)(4x + 8) = 0

Reorder the terms:
(-5 + 6x)(4x + 8) = 0

Reorder the terms:
(-5 + 6x)(8 + 4x) = 0

Multiply (-5 + 6x) * (8 + 4x)
(-5(8 + 4x) + 6x * (8 + 4x)) = 0
((8 * -5 + 4x * -5) + 6x * (8 + 4x)) = 0
((-40 + -20x) + 6x * (8 + 4x)) = 0
(-40 + -20x + (8 * 6x + 4x * 6x)) = 0
(-40 + -20x + (48x + 24x2)) = 0

Combine like terms: -20x + 48x = 28x
(-40 + 28x + 24x2) = 0

Solving
-40 + 28x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 7x + 6x2) = 0

Factor a trinomial.
4((-2 + -1x)(5 + -6x)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-2, 0.8333333333}

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