15600=(200-10x)(90+5x)

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Solution for 15600=(200-10x)(90+5x) equation: 


Simplifying
15600 = (200 + -10x)(90 + 5x)

Multiply (200 + -10x) * (90 + 5x)
15600 = (200(90 + 5x) + -10x * (90 + 5x))
15600 = ((90 * 200 + 5x * 200) + -10x * (90 + 5x))
15600 = ((18000 + 1000x) + -10x * (90 + 5x))
15600 = (18000 + 1000x + (90 * -10x + 5x * -10x))
15600 = (18000 + 1000x + (-900x + -50x2))

Combine like terms: 1000x + -900x = 100x
15600 = (18000 + 100x + -50x2)

Solving
15600 = 18000 + 100x + -50x2

Solving for variable 'x'.

Combine like terms: 15600 + -18000 = -2400
-2400 + -100x + 50x2 = 18000 + 100x + -50x2 + -18000 + -100x + 50x2

Reorder the terms:
-2400 + -100x + 50x2 = 18000 + -18000 + 100x + -100x + -50x2 + 50x2

Combine like terms: 18000 + -18000 = 0
-2400 + -100x + 50x2 = 0 + 100x + -100x + -50x2 + 50x2
-2400 + -100x + 50x2 = 100x + -100x + -50x2 + 50x2

Combine like terms: 100x + -100x = 0
-2400 + -100x + 50x2 = 0 + -50x2 + 50x2
-2400 + -100x + 50x2 = -50x2 + 50x2

Combine like terms: -50x2 + 50x2 = 0
-2400 + -100x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '50'.
50(-48 + -2x + x2) = 0

Factor a trinomial.
50((-6 + -1x)(8 + -1x)) = 0

Ignore the factor 50.

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
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
Solution
x = {-6, 8}

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