7t^2+21t-126=0

Solution for 7t^2+21t-126=0 equation:

Simplifying
7t2 + 21t + -126 = 0

Reorder the terms:
-126 + 21t + 7t2 = 0

Solving
-126 + 21t + 7t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-18 + 3t + t2) = 0

Factor a trinomial.
7((-6 + -1t)(3 + -1t)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 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 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
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 = {-6, 3}