6t^2-9t=4t-6

Solution for 6t^2-9t=4t-6 equation:

Simplifying
6t2 + -9t = 4t + -6

Reorder the terms:
-9t + 6t2 = 4t + -6

Reorder the terms:
-9t + 6t2 = -6 + 4t

Solving
-9t + 6t2 = -6 + 4t

Solving for variable 't'.

Reorder the terms:
6 + -9t + -4t + 6t2 = -6 + 4t + 6 + -4t

Combine like terms: -9t + -4t = -13t
6 + -13t + 6t2 = -6 + 4t + 6 + -4t

Reorder the terms:
6 + -13t + 6t2 = -6 + 6 + 4t + -4t

Combine like terms: -6 + 6 = 0
6 + -13t + 6t2 = 0 + 4t + -4t
6 + -13t + 6t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
6 + -13t + 6t2 = 0

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

Subproblem 1
Set the factor '(2 + -3t)' equal to zero and attempt to solve:

Simplifying
2 + -3t = 0

Solving
2 + -3t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

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

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {0.6666666667, 1.5}