3t^2+8t=t^2-3t-12

Solution for 3t^2+8t=t^2-3t-12 equation:

Simplifying
3t2 + 8t = t2 + -3t + -12

Reorder the terms:
8t + 3t2 = t2 + -3t + -12

Reorder the terms:
8t + 3t2 = -12 + -3t + t2

Solving
8t + 3t2 = -12 + -3t + t2

Solving for variable 't'.

Reorder the terms:
12 + 8t + 3t + 3t2 + -1t2 = -12 + -3t + t2 + 12 + 3t + -1t2

Combine like terms: 8t + 3t = 11t
12 + 11t + 3t2 + -1t2 = -12 + -3t + t2 + 12 + 3t + -1t2

Combine like terms: 3t2 + -1t2 = 2t2
12 + 11t + 2t2 = -12 + -3t + t2 + 12 + 3t + -1t2

Reorder the terms:
12 + 11t + 2t2 = -12 + 12 + -3t + 3t + t2 + -1t2

Combine like terms: -12 + 12 = 0
12 + 11t + 2t2 = 0 + -3t + 3t + t2 + -1t2
12 + 11t + 2t2 = -3t + 3t + t2 + -1t2

Combine like terms: -3t + 3t = 0
12 + 11t + 2t2 = 0 + t2 + -1t2
12 + 11t + 2t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
12 + 11t + 2t2 = 0

Factor a trinomial.
(4 + t)(3 + 2t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {-4, -1.5}