5t^2-16t=-12

Solution for 5t^2-16t=-12 equation:

Simplifying
5t2 + -16t = -12

Reorder the terms:
-16t + 5t2 = -12

Solving
-16t + 5t2 = -12

Solving for variable 't'.

Reorder the terms:
12 + -16t + 5t2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -16t + 5t2 = 0

Factor a trinomial.
(6 + -5t)(2 + -1t) = 0

Subproblem 1
Set the factor '(6 + -5t)' equal to zero and attempt to solve:

Simplifying
6 + -5t = 0

Solving
6 + -5t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5t = 0 + -6
-5t = 0 + -6

Combine like terms: 0 + -6 = -6
-5t = -6

Divide each side by '-5'.
t = 1.2

Simplifying
t = 1.2
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {1.2, 2}