3000=(15-.50x)(200+8x)

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Solution for 3000=(15-.50x)(200+8x) equation: 


Simplifying
3000 = (15 + -0.50x)(200 + 8x)

Multiply (15 + -0.50x) * (200 + 8x)
3000 = (15(200 + 8x) + -0.50x * (200 + 8x))
3000 = ((200 * 15 + 8x * 15) + -0.50x * (200 + 8x))
3000 = ((3000 + 120x) + -0.50x * (200 + 8x))
3000 = (3000 + 120x + (200 * -0.50x + 8x * -0.50x))
3000 = (3000 + 120x + (-100x + -4x2))

Combine like terms: 120x + -100x = 20x
3000 = (3000 + 20x + -4x2)

Add '-3000' to each side of the equation.
3000 + -3000 = 3000 + 20x + -3000 + -4x2

Combine like terms: 3000 + -3000 = 0
0 = 3000 + 20x + -3000 + -4x2

Reorder the terms:
0 = 3000 + -3000 + 20x + -4x2

Combine like terms: 3000 + -3000 = 0
0 = 0 + 20x + -4x2
0 = 20x + -4x2

Solving
0 = 20x + -4x2

Solving for variable 'x'.
Remove the zero:
-20x + 4x2 = 20x + -4x2 + -20x + 4x2

Reorder the terms:
-20x + 4x2 = 20x + -20x + -4x2 + 4x2

Combine like terms: 20x + -20x = 0
-20x + 4x2 = 0 + -4x2 + 4x2
-20x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-20x + 4x2 = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Solution
x = {0, 5}

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