6t^2=-t+2

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

Simplifying
6t2 = -1t + 2

Reorder the terms:
6t2 = 2 + -1t

Solving
6t2 = 2 + -1t

Solving for variable 't'.

Reorder the terms:
-2 + t + 6t2 = 2 + -1t + -2 + t

Reorder the terms:
-2 + t + 6t2 = 2 + -2 + -1t + t

Combine like terms: 2 + -2 = 0
-2 + t + 6t2 = 0 + -1t + t
-2 + t + 6t2 = -1t + t

Combine like terms: -1t + t = 0
-2 + t + 6t2 = 0

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

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

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {-0.6666666667, 0.5}