0=t^2+12t+32

Solution for 0=t^2+12t+32 equation:

Simplifying
0 = t2 + 12t + 32

Reorder the terms:
0 = 32 + 12t + t2

Solving
0 = 32 + 12t + t2

Solving for variable 't'.

Combine like terms: 0 + -32 = -32
-32 + -12t + -1t2 = 32 + 12t + t2 + -32 + -12t + -1t2

Reorder the terms:
-32 + -12t + -1t2 = 32 + -32 + 12t + -12t + t2 + -1t2

Combine like terms: 32 + -32 = 0
-32 + -12t + -1t2 = 0 + 12t + -12t + t2 + -1t2
-32 + -12t + -1t2 = 12t + -12t + t2 + -1t2

Combine like terms: 12t + -12t = 0
-32 + -12t + -1t2 = 0 + t2 + -1t2
-32 + -12t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-32 + -12t + -1t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 12t + t2) = 0

Factor a trinomial.
-1((8 + t)(4 + t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + t)' equal to zero and attempt to solve:

Simplifying
8 + t = 0

Solving
8 + t = 0

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

Add '-8' to each side of the equation.
8 + -8 + t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + t = 0 + -8
t = 0 + -8

Combine like terms: 0 + -8 = -8
t = -8

Simplifying
t = -8
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 = {-8, -4}