t^2=18-3t

Solution for t^2=18-3t equation:

Simplifying
t2 = 18 + -3t

Solving
t2 = 18 + -3t

Solving for variable 't'.

Reorder the terms:
-18 + 3t + t2 = 18 + -3t + -18 + 3t

Reorder the terms:
-18 + 3t + t2 = 18 + -18 + -3t + 3t

Combine like terms: 18 + -18 = 0
-18 + 3t + t2 = 0 + -3t + 3t
-18 + 3t + t2 = -3t + 3t

Combine like terms: -3t + 3t = 0
-18 + 3t + t2 = 0

Factor a trinomial.
(-6 + -1t)(3 + -1t) = 0

Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 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 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
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 = {-6, 3}