-t^2+5t+42=6

Solution for -t^2+5t+42=6 equation:

Simplifying
-1t2 + 5t + 42 = 6

Reorder the terms:
42 + 5t + -1t2 = 6

Solving
42 + 5t + -1t2 = 6

Solving for variable 't'.

Reorder the terms:
42 + -6 + 5t + -1t2 = 6 + -6

Combine like terms: 42 + -6 = 36
36 + 5t + -1t2 = 6 + -6

Combine like terms: 6 + -6 = 0
36 + 5t + -1t2 = 0

Factor a trinomial.
(9 + -1t)(4 + t) = 0

Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 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 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4
Solution
t = {9, -4}