5(t^2-2)*2t=t(t-1)

Solution for 5(t^2-2)*2t=t(t-1) equation:

Simplifying
5(t2 + -2) * 2t = t(t + -1)

Reorder the terms:
5(-2 + t2) * 2t = t(t + -1)

Reorder the terms for easier multiplication:
5 * 2t(-2 + t2) = t(t + -1)

Multiply 5 * 2
10t(-2 + t2) = t(t + -1)
(-2 * 10t + t2 * 10t) = t(t + -1)
(-20t + 10t3) = t(t + -1)

Reorder the terms:
-20t + 10t3 = t(-1 + t)
-20t + 10t3 = (-1 * t + t * t)
-20t + 10t3 = (-1t + t2)

Solving
-20t + 10t3 = -1t + t2

Solving for variable 't'.

Reorder the terms:
-20t + t + -1t2 + 10t3 = -1t + t2 + t + -1t2

Combine like terms: -20t + t = -19t
-19t + -1t2 + 10t3 = -1t + t2 + t + -1t2

Reorder the terms:
-19t + -1t2 + 10t3 = -1t + t + t2 + -1t2

Combine like terms: -1t + t = 0
-19t + -1t2 + 10t3 = 0 + t2 + -1t2
-19t + -1t2 + 10t3 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-19t + -1t2 + 10t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-19 + -1t + 10t2) = 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 '(-19 + -1t + 10t2)' equal to zero and attempt to solve:

Simplifying
-19 + -1t + 10t2 = 0

Solving
-19 + -1t + 10t2 = 0

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

Divide each side by '10'.
-1.9 + -0.1t + t2 = 0.0

Move the constant term to the right:

Add '1.9' to each side of the equation.
-1.9 + -0.1t + 1.9 + t2 = 0.0 + 1.9

Reorder the terms:
-1.9 + 1.9 + -0.1t + t2 = 0.0 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + -0.1t + t2 = 0.0 + 1.9
-0.1t + t2 = 0.0 + 1.9

Combine like terms: 0.0 + 1.9 = 1.9
-0.1t + t2 = 1.9

The t term is -0.1t.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1t + 0.0025 + t2 = 1.9 + 0.0025

Reorder the terms:
0.0025 + -0.1t + t2 = 1.9 + 0.0025

Combine like terms: 1.9 + 0.0025 = 1.9025
0.0025 + -0.1t + t2 = 1.9025

Factor a perfect square on the left side:
(t + -0.05)(t + -0.05) = 1.9025

Calculate the square root of the right side: 1.379311422

Break this problem into two subproblems by setting 
(t + -0.05) equal to 1.379311422 and -1.379311422.

Subproblem 1
t + -0.05 = 1.379311422

Simplifying
t + -0.05 = 1.379311422

Reorder the terms:
-0.05 + t = 1.379311422

Solving
-0.05 + t = 1.379311422

Solving for variable 't'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + t = 1.379311422 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + t = 1.379311422 + 0.05
t = 1.379311422 + 0.05

Combine like terms: 1.379311422 + 0.05 = 1.429311422
t = 1.429311422

Simplifying
t = 1.429311422

Subproblem 2
t + -0.05 = -1.379311422

Simplifying
t + -0.05 = -1.379311422

Reorder the terms:
-0.05 + t = -1.379311422

Solving
-0.05 + t = -1.379311422

Solving for variable 't'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + t = -1.379311422 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + t = -1.379311422 + 0.05
t = -1.379311422 + 0.05

Combine like terms: -1.379311422 + 0.05 = -1.329311422
t = -1.329311422

Simplifying
t = -1.329311422

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.429311422, -1.329311422}
Solution
t = {0, 1.429311422, -1.329311422}