0=3x^2-18x-81

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Solution for 0=3x^2-18x-81 equation:


Simplifying
0 = 3x2 + -18x + -81

Reorder the terms:
0 = -81 + -18x + 3x2

Solving
0 = -81 + -18x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 81 = 81
81 + 18x + -3x2 = -81 + -18x + 3x2 + 81 + 18x + -3x2

Reorder the terms:
81 + 18x + -3x2 = -81 + 81 + -18x + 18x + 3x2 + -3x2

Combine like terms: -81 + 81 = 0
81 + 18x + -3x2 = 0 + -18x + 18x + 3x2 + -3x2
81 + 18x + -3x2 = -18x + 18x + 3x2 + -3x2

Combine like terms: -18x + 18x = 0
81 + 18x + -3x2 = 0 + 3x2 + -3x2
81 + 18x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
81 + 18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + 6x + -1x2) = 0

Factor a trinomial.
3((9 + -1x)(3 + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {9, -3}

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