2t^2+15t+7=0

Solution for 2t^2+15t+7=0 equation:

Simplifying
2t2 + 15t + 7 = 0

Reorder the terms:
7 + 15t + 2t2 = 0

Solving
7 + 15t + 2t2 = 0

Solving for variable 't'.

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

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

Simplifying
7 + t = 0

Solving
7 + t = 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 + t = 0 + -7

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

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

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

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-7, -0.5}