10t^2+33t-54=0

Solution for 10t^2+33t-54=0 equation:

Simplifying
10t2 + 33t + -54 = 0

Reorder the terms:
-54 + 33t + 10t2 = 0

Solving
-54 + 33t + 10t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + -2t)(6 + -5t) = 0

Subproblem 1
Set the factor '(-9 + -2t)' equal to zero and attempt to solve:

Simplifying
-9 + -2t = 0

Solving
-9 + -2t = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2t = 0 + 9
-2t = 0 + 9

Combine like terms: 0 + 9 = 9
-2t = 9

Divide each side by '-2'.
t = -4.5

Simplifying
t = -4.5
Subproblem 2
Set the factor '(6 + -5t)' equal to zero and attempt to solve:

Simplifying
6 + -5t = 0

Solving
6 + -5t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5t = 0 + -6
-5t = 0 + -6

Combine like terms: 0 + -6 = -6
-5t = -6

Divide each side by '-5'.
t = 1.2

Simplifying
t = 1.2
Solution
t = {-4.5, 1.2}