22t-6t^2=-8

Solution for 22t-6t^2=-8 equation:

Simplifying
22t + -6t2 = -8

Solving
22t + -6t2 = -8

Solving for variable 't'.

Reorder the terms:
8 + 22t + -6t2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 22t + -6t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 11t + -3t2) = 0

Factor a trinomial.
2((4 + -1t)(1 + 3t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
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 = {4, -0.3333333333}