t(t+3)+t^2-9=0

Solution for t(t+3)+t^2-9=0 equation:

Simplifying
t(t + 3) + t2 + -9 = 0

Reorder the terms:
t(3 + t) + t2 + -9 = 0
(3 * t + t * t) + t2 + -9 = 0
(3t + t2) + t2 + -9 = 0

Reorder the terms:
-9 + 3t + t2 + t2 = 0

Combine like terms: t2 + t2 = 2t2
-9 + 3t + 2t2 = 0

Solving
-9 + 3t + 2t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -1t)(3 + -2t) = 0

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 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 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
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 = {-3, 1.5}