(5x+40)(4x-2)=0

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Solution for (5x+40)(4x-2)=0 equation: 


Simplifying
(5x + 40)(4x + -2) = 0

Reorder the terms:
(40 + 5x)(4x + -2) = 0

Reorder the terms:
(40 + 5x)(-2 + 4x) = 0

Multiply (40 + 5x) * (-2 + 4x)
(40(-2 + 4x) + 5x * (-2 + 4x)) = 0
((-2 * 40 + 4x * 40) + 5x * (-2 + 4x)) = 0
((-80 + 160x) + 5x * (-2 + 4x)) = 0
(-80 + 160x + (-2 * 5x + 4x * 5x)) = 0
(-80 + 160x + (-10x + 20x2)) = 0

Combine like terms: 160x + -10x = 150x
(-80 + 150x + 20x2) = 0

Solving
-80 + 150x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + 15x + 2x2) = 0

Factor a trinomial.
10((-8 + -1x)(1 + -2x)) = 0

Ignore the factor 10.

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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-8, 0.5}

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