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

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


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

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

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

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

Combine like terms: 32x + -30x = 2x
(-40 + 2x + 24x2) = 0

Solving
-40 + 2x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + x + 12x2) = 0

Factor a trinomial.
2((-4 + -3x)(5 + -4x)) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-1.333333333, 1.25}

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