t=10t^2+2t+3

Solution for t=10t^2+2t+3 equation:

Simplifying
t = 10t2 + 2t + 3

Reorder the terms:
t = 3 + 2t + 10t2

Solving
t = 3 + 2t + 10t2

Solving for variable 't'.

Reorder the terms:
-3 + t + -2t + -10t2 = 3 + 2t + 10t2 + -3 + -2t + -10t2

Combine like terms: t + -2t = -1t
-3 + -1t + -10t2 = 3 + 2t + 10t2 + -3 + -2t + -10t2

Reorder the terms:
-3 + -1t + -10t2 = 3 + -3 + 2t + -2t + 10t2 + -10t2

Combine like terms: 3 + -3 = 0
-3 + -1t + -10t2 = 0 + 2t + -2t + 10t2 + -10t2
-3 + -1t + -10t2 = 2t + -2t + 10t2 + -10t2

Combine like terms: 2t + -2t = 0
-3 + -1t + -10t2 = 0 + 10t2 + -10t2
-3 + -1t + -10t2 = 10t2 + -10t2

Combine like terms: 10t2 + -10t2 = 0
-3 + -1t + -10t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + t + 10t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + t + 10t2)' equal to zero and attempt to solve:

Simplifying
3 + t + 10t2 = 0

Solving
3 + t + 10t2 = 0

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

Divide each side by '10'.
0.3 + 0.1t + t2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 0.1t + -0.3 + t2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + 0.1t + t2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 0.1t + t2 = 0.0 + -0.3
0.1t + t2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
0.1t + t2 = -0.3

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.
0.1t + 0.25 + t2 = -0.3 + 0.25

Reorder the terms:
0.25 + 0.1t + t2 = -0.3 + 0.25

Combine like terms: -0.3 + 0.25 = -0.05
0.25 + 0.1t + t2 = -0.05

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -0.05

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.