3t^2-13t=10

Solution for 3t^2-13t=10 equation:

Simplifying
3t2 + -13t = 10

Reorder the terms:
-13t + 3t2 = 10

Solving
-13t + 3t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + -13t + 3t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -13t + 3t2 = 0

Factor a trinomial.
(-2 + -3t)(5 + -1t) = 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 '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-0.6666666667, 5}