0=30x^2-27x-66

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Solution for 0=30x^2-27x-66 equation:


Simplifying
0 = 30x2 + -27x + -66

Reorder the terms:
0 = -66 + -27x + 30x2

Solving
0 = -66 + -27x + 30x2

Solving for variable 'x'.

Combine like terms: 0 + 66 = 66
66 + 27x + -30x2 = -66 + -27x + 30x2 + 66 + 27x + -30x2

Reorder the terms:
66 + 27x + -30x2 = -66 + 66 + -27x + 27x + 30x2 + -30x2

Combine like terms: -66 + 66 = 0
66 + 27x + -30x2 = 0 + -27x + 27x + 30x2 + -30x2
66 + 27x + -30x2 = -27x + 27x + 30x2 + -30x2

Combine like terms: -27x + 27x = 0
66 + 27x + -30x2 = 0 + 30x2 + -30x2
66 + 27x + -30x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
66 + 27x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(22 + 9x + -10x2) = 0

Factor a trinomial.
3((2 + -1x)(11 + 10x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(11 + 10x)' equal to zero and attempt to solve:

Simplifying
11 + 10x = 0

Solving
11 + 10x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + 10x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 10x = 0 + -11
10x = 0 + -11

Combine like terms: 0 + -11 = -11
10x = -11

Divide each side by '10'.
x = -1.1

Simplifying
x = -1.1
Solution
x = {2, -1.1}

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