12=-5t^2-2t+36

Solution for 12=-5t^2-2t+36 equation:

Simplifying
12 = -5t2 + -2t + 36

Reorder the terms:
12 = 36 + -2t + -5t2

Solving
12 = 36 + -2t + -5t2

Solving for variable 't'.

Combine like terms: 12 + -36 = -24
-24 + 2t + 5t2 = 36 + -2t + -5t2 + -36 + 2t + 5t2

Reorder the terms:
-24 + 2t + 5t2 = 36 + -36 + -2t + 2t + -5t2 + 5t2

Combine like terms: 36 + -36 = 0
-24 + 2t + 5t2 = 0 + -2t + 2t + -5t2 + 5t2
-24 + 2t + 5t2 = -2t + 2t + -5t2 + 5t2

Combine like terms: -2t + 2t = 0
-24 + 2t + 5t2 = 0 + -5t2 + 5t2
-24 + 2t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-24 + 2t + 5t2 = 0

Factor a trinomial.
(-12 + -5t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-12 + -5t)' equal to zero and attempt to solve:

Simplifying
-12 + -5t = 0

Solving
-12 + -5t = 0

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

Add '12' to each side of the equation.
-12 + 12 + -5t = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5t = 0 + 12
-5t = 0 + 12

Combine like terms: 0 + 12 = 12
-5t = 12

Divide each side by '-5'.
t = -2.4

Simplifying
t = -2.4
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-2.4, 2}