4t^2-22t=-30

Solution for 4t^2-22t=-30 equation:

Simplifying
4t2 + -22t = -30

Reorder the terms:
-22t + 4t2 = -30

Solving
-22t + 4t2 = -30

Solving for variable 't'.

Reorder the terms:
30 + -22t + 4t2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -22t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -11t + 2t2) = 0

Factor a trinomial.
2((5 + -2t)(3 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 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 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {2.5, 3}