7t=12+t^2

Solution for 7t=12+t^2 equation:

Simplifying
7t = 12 + t2

Solving
7t = 12 + t2

Solving for variable 't'.

Reorder the terms:
-12 + 7t + -1t2 = 12 + t2 + -12 + -1t2

Reorder the terms:
-12 + 7t + -1t2 = 12 + -12 + t2 + -1t2

Combine like terms: 12 + -12 = 0
-12 + 7t + -1t2 = 0 + t2 + -1t2
-12 + 7t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-12 + 7t + -1t2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
t = {4, 3}