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

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


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

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

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

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

Combine like terms: -40x + 24x = -16x
(-20 + -16x + 48x2) = 0

Solving
-20 + -16x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -4x + 12x2) = 0

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

Ignore the factor 4.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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 = {-0.5, 0.8333333333}

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