(t^2)+t-42=0

Solution for (t^2)+t-42=0 equation:

Simplifying
(t2) + t + -42 = 0
t2 + t + -42 = 0

Reorder the terms:
-42 + t + t2 = 0

Solving
-42 + t + t2 = 0

Solving for variable 't'.

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

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

Simplifying
-7 + -1t = 0

Solving
-7 + -1t = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1t = 0 + 7
-1t = 0 + 7

Combine like terms: 0 + 7 = 7
-1t = 7

Divide each side by '-1'.
t = -7

Simplifying
t = -7
Subproblem 2
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
Solution
t = {-7, 6}