t*t=t+12

Solution for t*t=t+12 equation:

Simplifying
t * t = t + 12

Multiply t * t
t2 = t + 12

Reorder the terms:
t2 = 12 + t

Solving
t2 = 12 + t

Solving for variable 't'.

Reorder the terms:
-12 + -1t + t2 = 12 + t + -12 + -1t

Reorder the terms:
-12 + -1t + t2 = 12 + -12 + t + -1t

Combine like terms: 12 + -12 = 0
-12 + -1t + t2 = 0 + t + -1t
-12 + -1t + t2 = t + -1t

Combine like terms: t + -1t = 0
-12 + -1t + t2 = 0

Factor a trinomial.
(-3 + -1t)(4 + -1t) = 0

Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve:

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
Subproblem 2
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
Solution
t = {-3, 4}