12t^2+62t-22=0

Solution for 12t^2+62t-22=0 equation:

Simplifying
12t2 + 62t + -22 = 0

Reorder the terms:
-22 + 62t + 12t2 = 0

Solving
-22 + 62t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 31t + 6t2) = 0

Factor a trinomial.
2((-11 + -2t)(1 + -3t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -2t)' equal to zero and attempt to solve:

Simplifying
-11 + -2t = 0

Solving
-11 + -2t = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2t = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2t = 0 + 11
-2t = 0 + 11

Combine like terms: 0 + 11 = 11
-2t = 11

Divide each side by '-2'.
t = -5.5

Simplifying
t = -5.5
Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

Solving
1 + -3t = 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 + -3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3t = 0 + -1
-3t = 0 + -1

Combine like terms: 0 + -1 = -1
-3t = -1

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {-5.5, 0.3333333333}