6x^2=66x-60

Solution for 6x^2=66x-60 equation:

Simplifying
6x2 = 66x + -60

Reorder the terms:
6x2 = -60 + 66x

Solving
6x2 = -60 + 66x

Solving for variable 'x'.

Reorder the terms:
60 + -66x + 6x2 = -60 + 66x + 60 + -66x

Reorder the terms:
60 + -66x + 6x2 = -60 + 60 + 66x + -66x

Combine like terms: -60 + 60 = 0
60 + -66x + 6x2 = 0 + 66x + -66x
60 + -66x + 6x2 = 66x + -66x

Combine like terms: 66x + -66x = 0
60 + -66x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(10 + -11x + x2) = 0

Factor a trinomial.
6((1 + -1x)(10 + -1x)) = 0

Ignore the factor 6.
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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {1, 10}