(5x-10)(2x+8)=0

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Solution for (5x-10)(2x+8)=0 equation: 


Simplifying
(5x + -10)(2x + 8) = 0

Reorder the terms:
(-10 + 5x)(2x + 8) = 0

Reorder the terms:
(-10 + 5x)(8 + 2x) = 0

Multiply (-10 + 5x) * (8 + 2x)
(-10(8 + 2x) + 5x * (8 + 2x)) = 0
((8 * -10 + 2x * -10) + 5x * (8 + 2x)) = 0
((-80 + -20x) + 5x * (8 + 2x)) = 0
(-80 + -20x + (8 * 5x + 2x * 5x)) = 0
(-80 + -20x + (40x + 10x2)) = 0

Combine like terms: -20x + 40x = 20x
(-80 + 20x + 10x2) = 0

Solving
-80 + 20x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + 2x + x2) = 0

Factor a trinomial.
10((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 10.

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 + -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 = {-4, 2}

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