t^2+42=-13t

Solution for t^2+42=-13t equation:

Simplifying
t2 + 42 = -13t

Reorder the terms:
42 + t2 = -13t

Solving
42 + t2 = -13t

Solving for variable 't'.

Reorder the terms:
42 + 13t + t2 = -13t + 13t

Combine like terms: -13t + 13t = 0
42 + 13t + t2 = 0

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

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

Simplifying
7 + t = 0

Solving
7 + t = 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 + t = 0 + -7

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

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

Simplifying
t = -7
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 = {-7, -6}