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

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


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

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

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

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

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

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

Solving for variable 'x'.

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

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

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

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

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2

Subproblem 2
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
Solution
x = {-1.2, 2}

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