2t^2+5t+2=2

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

Simplifying
2t2 + 5t + 2 = 2

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

Add '-2' to each side of the equation.
2 + 5t + -2 + 2t2 = 2 + -2

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

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

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

Solving
5t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(5 + 2t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(5 + 2t)' equal to zero and attempt to solve:

Simplifying
5 + 2t = 0

Solving
5 + 2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2t = 0 + -5

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

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

Divide each side by '2'.
t = -2.5

Simplifying
t = -2.5
Solution
t = {0, -2.5}