12t^2+t=6

Solution for 12t^2+t=6 equation:

Simplifying
12t2 + t = 6

Reorder the terms:
t + 12t2 = 6

Solving
t + 12t2 = 6

Solving for variable 't'.

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

Combine like terms: 6 + -6 = 0
-6 + t + 12t2 = 0

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

Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve:

Simplifying
-3 + -4t = 0

Solving
-3 + -4t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4t = 0 + 3
-4t = 0 + 3

Combine like terms: 0 + 3 = 3
-4t = 3

Divide each side by '-4'.
t = -0.75

Simplifying
t = -0.75
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 = {-0.75, 0.6666666667}