2t^2+5t=-3

Solution for 2t^2+5t=-3 equation:

Simplifying
2t2 + 5t = -3

Reorder the terms:
5t + 2t2 = -3

Solving
5t + 2t2 = -3

Solving for variable 't'.

Reorder the terms:
3 + 5t + 2t2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 5t + 2t2 = 0

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

Subproblem 1
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
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 = {-1.5, -1}