180=18t+2t^2

Solution for 180=18t+2t^2 equation:

Simplifying
180 = 18t + 2t2

Solving
180 = 18t + 2t2

Solving for variable 't'.

Reorder the terms:
180 + -18t + -2t2 = 18t + -18t + 2t2 + -2t2

Combine like terms: 18t + -18t = 0
180 + -18t + -2t2 = 0 + 2t2 + -2t2
180 + -18t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
180 + -18t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(90 + -9t + -1t2) = 0

Factor a trinomial.
2((6 + -1t)(15 + t)) = 0

Ignore the factor 2.
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 '(15 + t)' equal to zero and attempt to solve:

Simplifying
15 + t = 0

Solving
15 + t = 0

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

Add '-15' to each side of the equation.
15 + -15 + t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + t = 0 + -15
t = 0 + -15

Combine like terms: 0 + -15 = -15
t = -15

Simplifying
t = -15
Solution
t = {6, -15}