-4(5t-2)9t=6t-2

Solution for -4(5t-2)9t=6t-2 equation:

Simplifying
-4(5t + -2) * 9t = 6t + -2

Reorder the terms:
-4(-2 + 5t) * 9t = 6t + -2

Reorder the terms for easier multiplication:
-4 * 9t(-2 + 5t) = 6t + -2

Multiply -4 * 9
-36t(-2 + 5t) = 6t + -2
(-2 * -36t + 5t * -36t) = 6t + -2
(72t + -180t2) = 6t + -2

Reorder the terms:
72t + -180t2 = -2 + 6t

Solving
72t + -180t2 = -2 + 6t

Solving for variable 't'.

Reorder the terms:
2 + 72t + -6t + -180t2 = -2 + 6t + 2 + -6t

Combine like terms: 72t + -6t = 66t
2 + 66t + -180t2 = -2 + 6t + 2 + -6t

Reorder the terms:
2 + 66t + -180t2 = -2 + 2 + 6t + -6t

Combine like terms: -2 + 2 = 0
2 + 66t + -180t2 = 0 + 6t + -6t
2 + 66t + -180t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
2 + 66t + -180t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 33t + -90t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 33t + -90t2)' equal to zero and attempt to solve:

Simplifying
1 + 33t + -90t2 = 0

Solving
1 + 33t + -90t2 = 0

Begin completing the square.  Divide all terms by
-90 the coefficient of the squared term: 

Divide each side by '-90'.
-0.01111111111 + -0.3666666667t + t2 = 0.0

Move the constant term to the right:

Add '0.01111111111' to each side of the equation.
-0.01111111111 + -0.3666666667t + 0.01111111111 + t2 = 0.0 + 0.01111111111

Reorder the terms:
-0.01111111111 + 0.01111111111 + -0.3666666667t + t2 = 0.0 + 0.01111111111

Combine like terms: -0.01111111111 + 0.01111111111 = 0.00000000000
0.00000000000 + -0.3666666667t + t2 = 0.0 + 0.01111111111
-0.3666666667t + t2 = 0.0 + 0.01111111111

Combine like terms: 0.0 + 0.01111111111 = 0.01111111111
-0.3666666667t + t2 = 0.01111111111

The t term is -0.3666666667t.  Take half its coefficient (-0.1833333334).
Square it (0.03361111114) and add it to both sides.

Add '0.03361111114' to each side of the equation.
-0.3666666667t + 0.03361111114 + t2 = 0.01111111111 + 0.03361111114

Reorder the terms:
0.03361111114 + -0.3666666667t + t2 = 0.01111111111 + 0.03361111114

Combine like terms: 0.01111111111 + 0.03361111114 = 0.04472222225
0.03361111114 + -0.3666666667t + t2 = 0.04472222225

Factor a perfect square on the left side:
(t + -0.1833333334)(t + -0.1833333334) = 0.04472222225

Calculate the square root of the right side: 0.211476292

Break this problem into two subproblems by setting 
(t + -0.1833333334) equal to 0.211476292 and -0.211476292.

Subproblem 1
t + -0.1833333334 = 0.211476292

Simplifying
t + -0.1833333334 = 0.211476292

Reorder the terms:
-0.1833333334 + t = 0.211476292

Solving
-0.1833333334 + t = 0.211476292

Solving for variable 't'.

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

Add '0.1833333334' to each side of the equation.
-0.1833333334 + 0.1833333334 + t = 0.211476292 + 0.1833333334

Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000
0.0000000000 + t = 0.211476292 + 0.1833333334
t = 0.211476292 + 0.1833333334

Combine like terms: 0.211476292 + 0.1833333334 = 0.3948096254
t = 0.3948096254

Simplifying
t = 0.3948096254

Subproblem 2
t + -0.1833333334 = -0.211476292

Simplifying
t + -0.1833333334 = -0.211476292

Reorder the terms:
-0.1833333334 + t = -0.211476292

Solving
-0.1833333334 + t = -0.211476292

Solving for variable 't'.

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

Add '0.1833333334' to each side of the equation.
-0.1833333334 + 0.1833333334 + t = -0.211476292 + 0.1833333334

Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000
0.0000000000 + t = -0.211476292 + 0.1833333334
t = -0.211476292 + 0.1833333334

Combine like terms: -0.211476292 + 0.1833333334 = -0.0281429586
t = -0.0281429586

Simplifying
t = -0.0281429586

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.3948096254, -0.0281429586}
Solution
t = {0.3948096254, -0.0281429586}