2t^2-3t-20=0

Solution for 2t^2-3t-20=0 equation:

Simplifying
2t2 + -3t + -20 = 0

Reorder the terms:
-20 + -3t + 2t2 = 0

Solving
-20 + -3t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -2t)(4 + -1t) = 0

Subproblem 1
Set the factor '(-5 + -2t)' equal to zero and attempt to solve:

Simplifying
-5 + -2t = 0

Solving
-5 + -2t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2t = 0 + 5
-2t = 0 + 5

Combine like terms: 0 + 5 = 5
-2t = 5

Divide each side by '-2'.
t = -2.5

Simplifying
t = -2.5
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

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

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-2.5, 4}