66=3x^2-18x+81

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Solution for 66=3x^2-18x+81 equation:


Simplifying
66 = 3x2 + -18x + 81

Reorder the terms:
66 = 81 + -18x + 3x2

Solving
66 = 81 + -18x + 3x2

Solving for variable 'x'.

Combine like terms: 66 + -81 = -15
-15 + 18x + -3x2 = 81 + -18x + 3x2 + -81 + 18x + -3x2

Reorder the terms:
-15 + 18x + -3x2 = 81 + -81 + -18x + 18x + 3x2 + -3x2

Combine like terms: 81 + -81 = 0
-15 + 18x + -3x2 = 0 + -18x + 18x + 3x2 + -3x2
-15 + 18x + -3x2 = -18x + 18x + 3x2 + -3x2

Combine like terms: -18x + 18x = 0
-15 + 18x + -3x2 = 0 + 3x2 + -3x2
-15 + 18x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-15 + 18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 6x + -1x2) = 0

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

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

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

Solution

x = {5, 1}

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