1500=(800-100x)x

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Solution for 1500=(800-100x)x equation:


Simplifying
1500 = (800 + -100x) * x

Reorder the terms for easier multiplication:
1500 = x(800 + -100x)
1500 = (800 * x + -100x * x)
1500 = (800x + -100x2)

Solving
1500 = 800x + -100x2

Solving for variable 'x'.

Reorder the terms:
1500 + -800x + 100x2 = 800x + -800x + -100x2 + 100x2

Combine like terms: 800x + -800x = 0
1500 + -800x + 100x2 = 0 + -100x2 + 100x2
1500 + -800x + 100x2 = -100x2 + 100x2

Combine like terms: -100x2 + 100x2 = 0
1500 + -800x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(15 + -8x + x2) = 0

Factor a trinomial.
100((3 + -1x)(5 + -1x)) = 0

Ignore the factor 100.

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {3, 5}

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