6t^2+25t-9=0

Solution for 6t^2+25t-9=0 equation:

Simplifying
6t2 + 25t + -9 = 0

Reorder the terms:
-9 + 25t + 6t2 = 0

Solving
-9 + 25t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + -2t)(1 + -3t) = 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 '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

Solving
1 + -3t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3t = 0 + -1

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

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

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {-4.5, 0.3333333333}