(10x-4)(2x+8)=0

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Solution for (10x-4)(2x+8)=0 equation: 


Simplifying
(10x + -4)(2x + 8) = 0

Reorder the terms:
(-4 + 10x)(2x + 8) = 0

Reorder the terms:
(-4 + 10x)(8 + 2x) = 0

Multiply (-4 + 10x) * (8 + 2x)
(-4(8 + 2x) + 10x * (8 + 2x)) = 0
((8 * -4 + 2x * -4) + 10x * (8 + 2x)) = 0
((-32 + -8x) + 10x * (8 + 2x)) = 0
(-32 + -8x + (8 * 10x + 2x * 10x)) = 0
(-32 + -8x + (80x + 20x2)) = 0

Combine like terms: -8x + 80x = 72x
(-32 + 72x + 20x2) = 0

Solving
-32 + 72x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 18x + 5x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-4, 0.4}

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