t^2-t=4t+36

Solution for t^2-t=4t+36 equation:

Simplifying
t2 + -1t = 4t + 36

Reorder the terms:
-1t + t2 = 4t + 36

Reorder the terms:
-1t + t2 = 36 + 4t

Solving
-1t + t2 = 36 + 4t

Solving for variable 't'.

Reorder the terms:
-36 + -1t + -4t + t2 = 36 + 4t + -36 + -4t

Combine like terms: -1t + -4t = -5t
-36 + -5t + t2 = 36 + 4t + -36 + -4t

Reorder the terms:
-36 + -5t + t2 = 36 + -36 + 4t + -4t

Combine like terms: 36 + -36 = 0
-36 + -5t + t2 = 0 + 4t + -4t
-36 + -5t + t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
-36 + -5t + t2 = 0

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

Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 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 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4
Subproblem 2
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
Solution
t = {-4, 9}