3750=300x-6x^2

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Solution for 3750=300x-6x^2 equation:


Simplifying
3750 = 300x + -6x2

Solving
3750 = 300x + -6x2

Solving for variable 'x'.

Reorder the terms:
3750 + -300x + 6x2 = 300x + -300x + -6x2 + 6x2

Combine like terms: 300x + -300x = 0
3750 + -300x + 6x2 = 0 + -6x2 + 6x2
3750 + -300x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
3750 + -300x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(625 + -50x + x2) = 0

Factor a trinomial.
6((25 + -1x)(25 + -1x)) = 0

Ignore the factor 6.

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 '(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

Solution

x = {25, 25}

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