t(2t+9)=-7

Solution for t(2t+9)=-7 equation:

Simplifying
t(2t + 9) = -7

Reorder the terms:
t(9 + 2t) = -7
(9 * t + 2t * t) = -7
(9t + 2t2) = -7

Solving
9t + 2t2 = -7

Solving for variable 't'.

Reorder the terms:
7 + 9t + 2t2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 9t + 2t2 = 0

Factor a trinomial.
(7 + 2t)(1 + t) = 0

Subproblem 1
Set the factor '(7 + 2t)' equal to zero and attempt to solve:

Simplifying
7 + 2t = 0

Solving
7 + 2t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2t = 0 + -7
2t = 0 + -7

Combine like terms: 0 + -7 = -7
2t = -7

Divide each side by '2'.
t = -3.5

Simplifying
t = -3.5
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

Simplifying
t = -1
Solution
t = {-3.5, -1}