49t^3+20t=-t^2

Solution for 49t^3+20t=-t^2 equation:

Simplifying
49t3 + 20t = -1t2

Reorder the terms:
20t + 49t3 = -1t2

Solving
20t + 49t3 = -1t2

Solving for variable 't'.

Reorder the terms:
20t + t2 + 49t3 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
20t + t2 + 49t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(20 + t + 49t2) = 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 '(20 + t + 49t2)' equal to zero and attempt to solve:

Simplifying
20 + t + 49t2 = 0

Solving
20 + t + 49t2 = 0

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

Divide each side by '49'.
0.4081632653 + 0.02040816327t + t2 = 0

Move the constant term to the right:

Add '-0.4081632653' to each side of the equation.
0.4081632653 + 0.02040816327t + -0.4081632653 + t2 = 0 + -0.4081632653

Reorder the terms:
0.4081632653 + -0.4081632653 + 0.02040816327t + t2 = 0 + -0.4081632653

Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000
0.0000000000 + 0.02040816327t + t2 = 0 + -0.4081632653
0.02040816327t + t2 = 0 + -0.4081632653

Combine like terms: 0 + -0.4081632653 = -0.4081632653
0.02040816327t + t2 = -0.4081632653

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.
0.02040816327t + 0.25 + t2 = -0.4081632653 + 0.25

Reorder the terms:
0.25 + 0.02040816327t + t2 = -0.4081632653 + 0.25

Combine like terms: -0.4081632653 + 0.25 = -0.1581632653
0.25 + 0.02040816327t + t2 = -0.1581632653

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -0.1581632653

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.
Solution
t = {0}