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

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


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

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

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

Multiply (-8 + 6x) * (4 + 5x)
(-8(4 + 5x) + 6x * (4 + 5x)) = 0
((4 * -8 + 5x * -8) + 6x * (4 + 5x)) = 0
((-32 + -40x) + 6x * (4 + 5x)) = 0
(-32 + -40x + (4 * 6x + 5x * 6x)) = 0
(-32 + -40x + (24x + 30x2)) = 0

Combine like terms: -40x + 24x = -16x
(-32 + -16x + 30x2) = 0

Solving
-32 + -16x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -8x + 15x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

Solving
-4 + -5x = 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 + -5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4

Combine like terms: 0 + 4 = 4
-5x = 4

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

Subproblem 2
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
Solution
x = {-0.8, 1.333333333}

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