316875=(450-3x)(200+16x)

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Solution for 316875=(450-3x)(200+16x) equation: 


Simplifying
316875 = (450 + -3x)(200 + 16x)

Multiply (450 + -3x) * (200 + 16x)
316875 = (450(200 + 16x) + -3x * (200 + 16x))
316875 = ((200 * 450 + 16x * 450) + -3x * (200 + 16x))
316875 = ((90000 + 7200x) + -3x * (200 + 16x))
316875 = (90000 + 7200x + (200 * -3x + 16x * -3x))
316875 = (90000 + 7200x + (-600x + -48x2))

Combine like terms: 7200x + -600x = 6600x
316875 = (90000 + 6600x + -48x2)

Solving
316875 = 90000 + 6600x + -48x2

Solving for variable 'x'.

Combine like terms: 316875 + -90000 = 226875
226875 + -6600x + 48x2 = 90000 + 6600x + -48x2 + -90000 + -6600x + 48x2

Reorder the terms:
226875 + -6600x + 48x2 = 90000 + -90000 + 6600x + -6600x + -48x2 + 48x2

Combine like terms: 90000 + -90000 = 0
226875 + -6600x + 48x2 = 0 + 6600x + -6600x + -48x2 + 48x2
226875 + -6600x + 48x2 = 6600x + -6600x + -48x2 + 48x2

Combine like terms: 6600x + -6600x = 0
226875 + -6600x + 48x2 = 0 + -48x2 + 48x2
226875 + -6600x + 48x2 = -48x2 + 48x2

Combine like terms: -48x2 + 48x2 = 0
226875 + -6600x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(75625 + -2200x + 16x2) = 0

Factor a trinomial.
3((275 + -4x)(275 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(275 + -4x)' equal to zero and attempt to solve:

Simplifying
275 + -4x = 0

Solving
275 + -4x = 0

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

Add '-275' to each side of the equation.
275 + -275 + -4x = 0 + -275

Combine like terms: 275 + -275 = 0
0 + -4x = 0 + -275
-4x = 0 + -275

Combine like terms: 0 + -275 = -275
-4x = -275

Divide each side by '-4'.
x = 68.75

Simplifying
x = 68.75

Subproblem 2
Set the factor '(275 + -4x)' equal to zero and attempt to solve:

Simplifying
275 + -4x = 0

Solving
275 + -4x = 0

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

Add '-275' to each side of the equation.
275 + -275 + -4x = 0 + -275

Combine like terms: 275 + -275 = 0
0 + -4x = 0 + -275
-4x = 0 + -275

Combine like terms: 0 + -275 = -275
-4x = -275

Divide each side by '-4'.
x = 68.75

Simplifying
x = 68.75
Solution
x = {68.75, 68.75}

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