(60-2x)(500+50x)=36400

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Solution for (60-2x)(500+50x)=36400 equation: 


Simplifying
(60 + -2x)(500 + 50x) = 36400

Multiply (60 + -2x) * (500 + 50x)
(60(500 + 50x) + -2x * (500 + 50x)) = 36400
((500 * 60 + 50x * 60) + -2x * (500 + 50x)) = 36400
((30000 + 3000x) + -2x * (500 + 50x)) = 36400
(30000 + 3000x + (500 * -2x + 50x * -2x)) = 36400
(30000 + 3000x + (-1000x + -100x2)) = 36400

Combine like terms: 3000x + -1000x = 2000x
(30000 + 2000x + -100x2) = 36400

Solving
30000 + 2000x + -100x2 = 36400

Solving for variable 'x'.

Reorder the terms:
30000 + -36400 + 2000x + -100x2 = 36400 + -36400

Combine like terms: 30000 + -36400 = -6400
-6400 + 2000x + -100x2 = 36400 + -36400

Combine like terms: 36400 + -36400 = 0
-6400 + 2000x + -100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(-64 + 20x + -1x2) = 0

Factor a trinomial.
100((-16 + x)(4 + -1x)) = 0

Ignore the factor 100.

Subproblem 1
Set the factor '(-16 + x)' equal to zero and attempt to solve:

Simplifying
-16 + x = 0

Solving
-16 + x = 0

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

Add '16' to each side of the equation.
-16 + 16 + x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + x = 0 + 16
x = 0 + 16

Combine like terms: 0 + 16 = 16
x = 16

Simplifying
x = 16

Subproblem 2
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
Solution
x = {16, 4}

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