0=2t^2+17t+36

Solution for 0=2t^2+17t+36 equation:

Simplifying
0 = 2t2 + 17t + 36

Reorder the terms:
0 = 36 + 17t + 2t2

Solving
0 = 36 + 17t + 2t2

Solving for variable 't'.

Combine like terms: 0 + -36 = -36
-36 + -17t + -2t2 = 36 + 17t + 2t2 + -36 + -17t + -2t2

Reorder the terms:
-36 + -17t + -2t2 = 36 + -36 + 17t + -17t + 2t2 + -2t2

Combine like terms: 36 + -36 = 0
-36 + -17t + -2t2 = 0 + 17t + -17t + 2t2 + -2t2
-36 + -17t + -2t2 = 17t + -17t + 2t2 + -2t2

Combine like terms: 17t + -17t = 0
-36 + -17t + -2t2 = 0 + 2t2 + -2t2
-36 + -17t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
-36 + -17t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 17t + 2t2) = 0

Factor a trinomial.
-1((9 + 2t)(4 + t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(9 + 2t)' equal to zero and attempt to solve:

Simplifying
9 + 2t = 0

Solving
9 + 2t = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2t = 0 + -9
2t = 0 + -9

Combine like terms: 0 + -9 = -9
2t = -9

Divide each side by '2'.
t = -4.5

Simplifying
t = -4.5
Subproblem 2
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
Solution
t = {-4.5, -4}