5t(t-2)=-3

Solution for 5t(t-2)=-3 equation:

Simplifying
5t(t + -2) = -3

Reorder the terms:
5t(-2 + t) = -3
(-2 * 5t + t * 5t) = -3
(-10t + 5t2) = -3

Solving
-10t + 5t2 = -3

Solving for variable 't'.

Reorder the terms:
3 + -10t + 5t2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -10t + 5t2 = 0

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

Divide each side by '5'.
0.6 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -2t + -0.6 + t2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -2t + t2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -2t + t2 = 0 + -0.6
-2t + t2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-2t + t2 = -0.6

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.6 + 1

Reorder the terms:
1 + -2t + t2 = -0.6 + 1

Combine like terms: -0.6 + 1 = 0.4
1 + -2t + t2 = 0.4

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(t + -1) equal to 0.632455532 and -0.632455532.

Subproblem 1
t + -1 = 0.632455532

Simplifying
t + -1 = 0.632455532

Reorder the terms:
-1 + t = 0.632455532

Solving
-1 + t = 0.632455532

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.632455532 + 1
t = 0.632455532 + 1

Combine like terms: 0.632455532 + 1 = 1.632455532
t = 1.632455532

Simplifying
t = 1.632455532

Subproblem 2
t + -1 = -0.632455532

Simplifying
t + -1 = -0.632455532

Reorder the terms:
-1 + t = -0.632455532

Solving
-1 + t = -0.632455532

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.632455532 + 1
t = -0.632455532 + 1

Combine like terms: -0.632455532 + 1 = 0.367544468
t = 0.367544468

Simplifying
t = 0.367544468

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.632455532, 0.367544468}