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

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


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

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

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

Multiply (-8 + 5x) * (8 + 4x)
(-8(8 + 4x) + 5x * (8 + 4x)) = 0
((8 * -8 + 4x * -8) + 5x * (8 + 4x)) = 0
((-64 + -32x) + 5x * (8 + 4x)) = 0
(-64 + -32x + (8 * 5x + 4x * 5x)) = 0
(-64 + -32x + (40x + 20x2)) = 0

Combine like terms: -32x + 40x = 8x
(-64 + 8x + 20x2) = 0

Solving
-64 + 8x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 2x + 5x2) = 0

Factor a trinomial.
4((-2 + -1x)(8 + -5x)) = 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 '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-2, 1.6}

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