2t^2-t-21=0

Solution for 2t^2-t-21=0 equation:

Simplifying
2t2 + -1t + -21 = 0

Reorder the terms:
-21 + -1t + 2t2 = 0

Solving
-21 + -1t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -1t)(7 + -2t) = 0

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 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 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
Subproblem 2
Set the factor '(7 + -2t)' equal to zero and attempt to solve:

Simplifying
7 + -2t = 0

Solving
7 + -2t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2t = 0 + -7
-2t = 0 + -7

Combine like terms: 0 + -7 = -7
-2t = -7

Divide each side by '-2'.
t = 3.5

Simplifying
t = 3.5
Solution
t = {-3, 3.5}