(5x+40)(4x-25)=0

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Solution for (5x+40)(4x-25)=0 equation: 


Simplifying
(5x + 40)(4x + -25) = 0

Reorder the terms:
(40 + 5x)(4x + -25) = 0

Reorder the terms:
(40 + 5x)(-25 + 4x) = 0

Multiply (40 + 5x) * (-25 + 4x)
(40(-25 + 4x) + 5x * (-25 + 4x)) = 0
((-25 * 40 + 4x * 40) + 5x * (-25 + 4x)) = 0
((-1000 + 160x) + 5x * (-25 + 4x)) = 0
(-1000 + 160x + (-25 * 5x + 4x * 5x)) = 0
(-1000 + 160x + (-125x + 20x2)) = 0

Combine like terms: 160x + -125x = 35x
(-1000 + 35x + 20x2) = 0

Solving
-1000 + 35x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-200 + 7x + 4x2) = 0

Factor a trinomial.
5((-8 + -1x)(25 + -4x)) = 0

Ignore the factor 5.

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 '(25 + -4x)' equal to zero and attempt to solve:

Simplifying
25 + -4x = 0

Solving
25 + -4x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -4x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -4x = 0 + -25
-4x = 0 + -25

Combine like terms: 0 + -25 = -25
-4x = -25

Divide each side by '-4'.
x = 6.25

Simplifying
x = 6.25
Solution
x = {-8, 6.25}

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