126=30+8t+4t^2

Solution for 126=30+8t+4t^2 equation:

Simplifying
126 = 30 + 8t + 4t2

Solving
126 = 30 + 8t + 4t2

Solving for variable 't'.

Combine like terms: 126 + -30 = 96
96 + -8t + -4t2 = 30 + 8t + 4t2 + -30 + -8t + -4t2

Reorder the terms:
96 + -8t + -4t2 = 30 + -30 + 8t + -8t + 4t2 + -4t2

Combine like terms: 30 + -30 = 0
96 + -8t + -4t2 = 0 + 8t + -8t + 4t2 + -4t2
96 + -8t + -4t2 = 8t + -8t + 4t2 + -4t2

Combine like terms: 8t + -8t = 0
96 + -8t + -4t2 = 0 + 4t2 + -4t2
96 + -8t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
96 + -8t + -4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + -2t + -1t2) = 0

Factor a trinomial.
4((4 + -1t)(6 + t)) = 0

Ignore the factor 4.
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 '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

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

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

Simplifying
t = -6
Solution
t = {4, -6}