3x^2-30x=-27

Solution for 3x^2-30x=-27 equation:

Simplifying
3x2 + -30x = -27

Reorder the terms:
-30x + 3x2 = -27

Solving
-30x + 3x2 = -27

Solving for variable 'x'.

Reorder the terms:
27 + -30x + 3x2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + -30x + 3x2 = 0

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

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
x = {1, 9}