2t-4t^2=10

Solution for 2t-4t^2=10 equation:

Simplifying
2t + -4t2 = 10

Solving
2t + -4t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + 2t + -4t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 2t + -4t2 = 0

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

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

Simplifying
-5 + t + -2t2 = 0

Solving
-5 + t + -2t2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
2.5 + -0.5t + t2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -0.5t + -2.5 + t2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -0.5t + t2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -0.5t + t2 = 0 + -2.5
-0.5t + t2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-0.5t + t2 = -2.5

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.
-0.5t + 0.25 + t2 = -2.5 + 0.25

Reorder the terms:
0.25 + -0.5t + t2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + -0.5t + t2 = -2.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -2.25

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.