2t=2+3t+5t^2

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

Simplifying
2t = 2 + 3t + 5t2

Solving
2t = 2 + 3t + 5t2

Solving for variable 't'.

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

Combine like terms: 2t + -3t = -1t
-2 + -1t + -5t2 = 2 + 3t + 5t2 + -2 + -3t + -5t2

Reorder the terms:
-2 + -1t + -5t2 = 2 + -2 + 3t + -3t + 5t2 + -5t2

Combine like terms: 2 + -2 = 0
-2 + -1t + -5t2 = 0 + 3t + -3t + 5t2 + -5t2
-2 + -1t + -5t2 = 3t + -3t + 5t2 + -5t2

Combine like terms: 3t + -3t = 0
-2 + -1t + -5t2 = 0 + 5t2 + -5t2
-2 + -1t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-2 + -1t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + t + 5t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + t + 5t2)' equal to zero and attempt to solve:

Simplifying
2 + t + 5t2 = 0

Solving
2 + t + 5t2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.4 + 0.2t + t2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 0.2t + -0.4 + t2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 0.2t + t2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 0.2t + t2 = 0 + -0.4
0.2t + t2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
0.2t + t2 = -0.4

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2t + 0.25 + t2 = -0.4 + 0.25

Reorder the terms:
0.25 + 0.2t + t2 = -0.4 + 0.25

Combine like terms: -0.4 + 0.25 = -0.15
0.25 + 0.2t + t2 = -0.15

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -0.15

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.