(500-20x)(45+5x)=0

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Solution for (500-20x)(45+5x)=0 equation: 


Simplifying
(500 + -20x)(45 + 5x) = 0

Multiply (500 + -20x) * (45 + 5x)
(500(45 + 5x) + -20x * (45 + 5x)) = 0
((45 * 500 + 5x * 500) + -20x * (45 + 5x)) = 0
((22500 + 2500x) + -20x * (45 + 5x)) = 0
(22500 + 2500x + (45 * -20x + 5x * -20x)) = 0
(22500 + 2500x + (-900x + -100x2)) = 0

Combine like terms: 2500x + -900x = 1600x
(22500 + 1600x + -100x2) = 0

Solving
22500 + 1600x + -100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '100'.
100(225 + 16x + -1x2) = 0

Factor a trinomial.
100((25 + -1x)(9 + x)) = 0

Ignore the factor 100.

Subproblem 1
Set the factor '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 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 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {25, -9}

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