6=2t^2+t

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

Simplifying
6 = 2t2 + t

Reorder the terms:
6 = t + 2t2

Solving
6 = t + 2t2

Solving for variable 't'.

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

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

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

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

Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

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

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

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Solution
t = {1.5, -2}