(5x+40)(4x-20)=0

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Solution for (5x+40)(4x-20)=0 equation: 


Simplifying
(5x + 40)(4x + -20) = 0

Reorder the terms:
(40 + 5x)(4x + -20) = 0

Reorder the terms:
(40 + 5x)(-20 + 4x) = 0

Multiply (40 + 5x) * (-20 + 4x)
(40(-20 + 4x) + 5x * (-20 + 4x)) = 0
((-20 * 40 + 4x * 40) + 5x * (-20 + 4x)) = 0
((-800 + 160x) + 5x * (-20 + 4x)) = 0
(-800 + 160x + (-20 * 5x + 4x * 5x)) = 0
(-800 + 160x + (-100x + 20x2)) = 0

Combine like terms: 160x + -100x = 60x
(-800 + 60x + 20x2) = 0

Solving
-800 + 60x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-40 + 3x + x2) = 0

Factor a trinomial.
20((-8 + -1x)(5 + -1x)) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-8, 5}

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