2t^2+3t-27=0

Solution for 2t^2+3t-27=0 equation:

Simplifying
2t2 + 3t + -27 = 0

Reorder the terms:
-27 + 3t + 2t2 = 0

Solving
-27 + 3t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + -2t)(3 + -1t) = 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 '(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
Solution
t = {-4.5, 3}