2t^2+12t=18t+108

Solution for 2t^2+12t=18t+108 equation:

Simplifying
2t2 + 12t = 18t + 108

Reorder the terms:
12t + 2t2 = 18t + 108

Reorder the terms:
12t + 2t2 = 108 + 18t

Solving
12t + 2t2 = 108 + 18t

Solving for variable 't'.

Reorder the terms:
-108 + 12t + -18t + 2t2 = 108 + 18t + -108 + -18t

Combine like terms: 12t + -18t = -6t
-108 + -6t + 2t2 = 108 + 18t + -108 + -18t

Reorder the terms:
-108 + -6t + 2t2 = 108 + -108 + 18t + -18t

Combine like terms: 108 + -108 = 0
-108 + -6t + 2t2 = 0 + 18t + -18t
-108 + -6t + 2t2 = 18t + -18t

Combine like terms: 18t + -18t = 0
-108 + -6t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -3t + t2) = 0

Factor a trinomial.
2((-6 + -1t)(9 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Solution
t = {-6, 9}