12t^2-5t+6=8

Solution for 12t^2-5t+6=8 equation:

Simplifying
12t2 + -5t + 6 = 8

Reorder the terms:
6 + -5t + 12t2 = 8

Solving
6 + -5t + 12t2 = 8

Solving for variable 't'.

Reorder the terms:
6 + -8 + -5t + 12t2 = 8 + -8

Combine like terms: 6 + -8 = -2
-2 + -5t + 12t2 = 8 + -8

Combine like terms: 8 + -8 = 0
-2 + -5t + 12t2 = 0

Factor a trinomial.
(-1 + -4t)(2 + -3t) = 0

Subproblem 1
Set the factor '(-1 + -4t)' equal to zero and attempt to solve:

Simplifying
-1 + -4t = 0

Solving
-1 + -4t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4t = 0 + 1
-4t = 0 + 1

Combine like terms: 0 + 1 = 1
-4t = 1

Divide each side by '-4'.
t = -0.25

Simplifying
t = -0.25
Subproblem 2
Set the factor '(2 + -3t)' equal to zero and attempt to solve:

Simplifying
2 + -3t = 0

Solving
2 + -3t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Solution
t = {-0.25, 0.6666666667}