12t^2-17t=5

Solution for 12t^2-17t=5 equation:

Simplifying
12t2 + -17t = 5

Reorder the terms:
-17t + 12t2 = 5

Solving
-17t + 12t2 = 5

Solving for variable 't'.

Reorder the terms:
-5 + -17t + 12t2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -17t + 12t2 = 0

Factor a trinomial.
(-1 + -4t)(5 + -3t) = 0

Subproblem 1
Set the factor '(-1 + -4t)' equal to zero and attempt to solve:

Simplifying
-1 + -4t = 0

Solving
-1 + -4t = 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 + -4t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4t = 0 + 1
-4t = 0 + 1

Combine like terms: 0 + 1 = 1
-4t = 1

Divide each side by '-4'.
t = -0.25

Simplifying
t = -0.25
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 = {-0.25, 1.666666667}