30x=x(120-x)

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Solution for 30x=x(120-x) equation:


Simplifying
30x = x(120 + -1x)
30x = (120 * x + -1x * x)
30x = (120x + -1x2)

Solving
30x = 120x + -1x2

Solving for variable 'x'.

Combine like terms: 30x + -120x = -90x
-90x + x2 = 120x + -1x2 + -120x + x2

Reorder the terms:
-90x + x2 = 120x + -120x + -1x2 + x2

Combine like terms: 120x + -120x = 0
-90x + x2 = 0 + -1x2 + x2
-90x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-90x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-90 + x) = 0

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 '(-90 + x)' equal to zero and attempt to solve: Simplifying -90 + x = 0 Solving -90 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 0 + 90 Combine like terms: -90 + 90 = 0 0 + x = 0 + 90 x = 0 + 90 Combine like terms: 0 + 90 = 90 x = 90 Simplifying x = 90

Solution

x = {0, 90}

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