3(2t^2-5)=t

Solution for 3(2t^2-5)=t equation:

Simplifying
3(2t2 + -5) = t

Reorder the terms:
3(-5 + 2t2) = t
(-5 * 3 + 2t2 * 3) = t
(-15 + 6t2) = t

Solving
-15 + 6t2 = t

Solving for variable 't'.

Reorder the terms:
-15 + -1t + 6t2 = t + -1t

Combine like terms: t + -1t = 0
-15 + -1t + 6t2 = 0

Factor a trinomial.
(-3 + -2t)(5 + -3t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve:

Simplifying
5 + -3t = 0

Solving
5 + -3t = 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 + -3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3t = 0 + -5
-3t = 0 + -5

Combine like terms: 0 + -5 = -5
-3t = -5

Divide each side by '-3'.
t = 1.666666667

Simplifying
t = 1.666666667
Solution
t = {-1.5, 1.666666667}