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

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

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

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

Reorder the terms for easier multiplication:
-5 * 3t(-2 + 3t) = 5t + -2

Multiply -5 * 3
-15t(-2 + 3t) = 5t + -2
(-2 * -15t + 3t * -15t) = 5t + -2
(30t + -45t2) = 5t + -2

Reorder the terms:
30t + -45t2 = -2 + 5t

Solving
30t + -45t2 = -2 + 5t

Solving for variable 't'.

Reorder the terms:
2 + 30t + -5t + -45t2 = -2 + 5t + 2 + -5t

Combine like terms: 30t + -5t = 25t
2 + 25t + -45t2 = -2 + 5t + 2 + -5t

Reorder the terms:
2 + 25t + -45t2 = -2 + 2 + 5t + -5t

Combine like terms: -2 + 2 = 0
2 + 25t + -45t2 = 0 + 5t + -5t
2 + 25t + -45t2 = 5t + -5t

Combine like terms: 5t + -5t = 0
2 + 25t + -45t2 = 0

Begin completing the square.  Divide all terms by
-45 the coefficient of the squared term: 

Divide each side by '-45'.
-0.04444444444 + -0.5555555556t + t2 = 0

Move the constant term to the right:

Add '0.04444444444' to each side of the equation.
-0.04444444444 + -0.5555555556t + 0.04444444444 + t2 = 0 + 0.04444444444

Reorder the terms:
-0.04444444444 + 0.04444444444 + -0.5555555556t + t2 = 0 + 0.04444444444

Combine like terms: -0.04444444444 + 0.04444444444 = 0.00000000000
0.00000000000 + -0.5555555556t + t2 = 0 + 0.04444444444
-0.5555555556t + t2 = 0 + 0.04444444444

Combine like terms: 0 + 0.04444444444 = 0.04444444444
-0.5555555556t + t2 = 0.04444444444

The t term is -0.5555555556t.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556t + 0.07716049384 + t2 = 0.04444444444 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556t + t2 = 0.04444444444 + 0.07716049384

Combine like terms: 0.04444444444 + 0.07716049384 = 0.12160493828
0.07716049384 + -0.5555555556t + t2 = 0.12160493828

Factor a perfect square on the left side:
(t + -0.2777777778)(t + -0.2777777778) = 0.12160493828

Calculate the square root of the right side: 0.348718996

Break this problem into two subproblems by setting 
(t + -0.2777777778) equal to 0.348718996 and -0.348718996.

Subproblem 1
t + -0.2777777778 = 0.348718996

Simplifying
t + -0.2777777778 = 0.348718996

Reorder the terms:
-0.2777777778 + t = 0.348718996

Solving
-0.2777777778 + t = 0.348718996

Solving for variable 't'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + t = 0.348718996 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + t = 0.348718996 + 0.2777777778
t = 0.348718996 + 0.2777777778

Combine like terms: 0.348718996 + 0.2777777778 = 0.6264967738
t = 0.6264967738

Simplifying
t = 0.6264967738

Subproblem 2
t + -0.2777777778 = -0.348718996

Simplifying
t + -0.2777777778 = -0.348718996

Reorder the terms:
-0.2777777778 + t = -0.348718996

Solving
-0.2777777778 + t = -0.348718996

Solving for variable 't'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + t = -0.348718996 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + t = -0.348718996 + 0.2777777778
t = -0.348718996 + 0.2777777778

Combine like terms: -0.348718996 + 0.2777777778 = -0.0709412182
t = -0.0709412182

Simplifying
t = -0.0709412182

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.6264967738, -0.0709412182}