t(t+4.1)=0.08t

Solution for t(t+4.1)=0.08t equation:

Simplifying
t(t + 4.1) = 0.08t

Reorder the terms:
t(4.1 + t) = 0.08t
(4.1 * t + t * t) = 0.08t
(4.1t + t2) = 0.08t

Solving
4.1t + t2 = 0.08t

Solving for variable 't'.

Reorder the terms:
4.1t + -0.08t + t2 = 0.08t + -0.08t

Combine like terms: 4.1t + -0.08t = 4.02t
4.02t + t2 = 0.08t + -0.08t

Combine like terms: 0.08t + -0.08t = 0.00
4.02t + t2 = 0.00

Factor out the Greatest Common Factor (GCF), 't'.
t(4.02 + t) = 0.00

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 '(4.02 + t)' equal to zero and attempt to solve:

Simplifying
4.02 + t = 0

Solving
4.02 + t = 0

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

Add '-4.02' to each side of the equation.
4.02 + -4.02 + t = 0 + -4.02

Combine like terms: 4.02 + -4.02 = 0.00
0.00 + t = 0 + -4.02
t = 0 + -4.02

Combine like terms: 0 + -4.02 = -4.02
t = -4.02

Simplifying
t = -4.02
Solution
t = {0, -4.02}