0=30x-x^2-81

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Solution for 0=30x-x^2-81 equation:


Simplifying
0 = 30x + -1x2 + -81

Reorder the terms:
0 = -81 + 30x + -1x2

Solving
0 = -81 + 30x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 81 = 81
81 + -30x + x2 = -81 + 30x + -1x2 + 81 + -30x + x2

Reorder the terms:
81 + -30x + x2 = -81 + 81 + 30x + -30x + -1x2 + x2

Combine like terms: -81 + 81 = 0
81 + -30x + x2 = 0 + 30x + -30x + -1x2 + x2
81 + -30x + x2 = 30x + -30x + -1x2 + x2

Combine like terms: 30x + -30x = 0
81 + -30x + x2 = 0 + -1x2 + x2
81 + -30x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
81 + -30x + x2 = 0

Factor a trinomial.
(3 + -1x)(27 + -1x) = 0

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 '(27 + -1x)' equal to zero and attempt to solve: Simplifying 27 + -1x = 0 Solving 27 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1x = 0 + -27 -1x = 0 + -27 Combine like terms: 0 + -27 = -27 -1x = -27 Divide each side by '-1'. x = 27 Simplifying x = 27

Solution

x = {3, 27}

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