(5x-4)(2x+4)=0

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Solution for (5x-4)(2x+4)=0 equation: 


Simplifying
(5x + -4)(2x + 4) = 0

Reorder the terms:
(-4 + 5x)(2x + 4) = 0

Reorder the terms:
(-4 + 5x)(4 + 2x) = 0

Multiply (-4 + 5x) * (4 + 2x)
(-4(4 + 2x) + 5x * (4 + 2x)) = 0
((4 * -4 + 2x * -4) + 5x * (4 + 2x)) = 0
((-16 + -8x) + 5x * (4 + 2x)) = 0
(-16 + -8x + (4 * 5x + 2x * 5x)) = 0
(-16 + -8x + (20x + 10x2)) = 0

Combine like terms: -8x + 20x = 12x
(-16 + 12x + 10x2) = 0

Solving
-16 + 12x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 6x + 5x2) = 0

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

Ignore the factor 2.

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 '(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
Solution
x = {-2, 0.8}

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