x(100-2x)=1200

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Solution for x(100-2x)=1200 equation:


Simplifying
x(100 + -2x) = 1200
(100 * x + -2x * x) = 1200
(100x + -2x2) = 1200

Solving
100x + -2x2 = 1200

Solving for variable 'x'.

Reorder the terms:
-1200 + 100x + -2x2 = 1200 + -1200

Combine like terms: 1200 + -1200 = 0
-1200 + 100x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-600 + 50x + -1x2) = 0

Factor a trinomial.
2((-30 + x)(20 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Simplifying x = 30

Subproblem 2

Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20

Solution

x = {30, 20}

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