t^2-4t-90=6

Solution for t^2-4t-90=6 equation:

Simplifying
t2 + -4t + -90 = 6

Reorder the terms:
-90 + -4t + t2 = 6

Solving
-90 + -4t + t2 = 6

Solving for variable 't'.

Reorder the terms:
-90 + -6 + -4t + t2 = 6 + -6

Combine like terms: -90 + -6 = -96
-96 + -4t + t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-96 + -4t + t2 = 0

Factor a trinomial.
(-8 + -1t)(12 + -1t) = 0

Subproblem 1
Set the factor '(-8 + -1t)' equal to zero and attempt to solve:

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t = 0 + 8
-1t = 0 + 8

Combine like terms: 0 + 8 = 8
-1t = 8

Divide each side by '-1'.
t = -8

Simplifying
t = -8
Subproblem 2
Set the factor '(12 + -1t)' equal to zero and attempt to solve:

Simplifying
12 + -1t = 0

Solving
12 + -1t = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1t = 0 + -12
-1t = 0 + -12

Combine like terms: 0 + -12 = -12
-1t = -12

Divide each side by '-1'.
t = 12

Simplifying
t = 12
Solution
t = {-8, 12}