75=3(10t-3)6t

Solution for 75=3(10t-3)6t equation:

Simplifying
75 = 3(10t + -3) * 6t

Reorder the terms:
75 = 3(-3 + 10t) * 6t

Reorder the terms for easier multiplication:
75 = 3 * 6t(-3 + 10t)

Multiply 3 * 6
75 = 18t(-3 + 10t)
75 = (-3 * 18t + 10t * 18t)
75 = (-54t + 180t2)

Solving
75 = -54t + 180t2

Solving for variable 't'.

Reorder the terms:
75 + 54t + -180t2 = -54t + 54t + 180t2 + -180t2

Combine like terms: -54t + 54t = 0
75 + 54t + -180t2 = 0 + 180t2 + -180t2
75 + 54t + -180t2 = 180t2 + -180t2

Combine like terms: 180t2 + -180t2 = 0
75 + 54t + -180t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + 18t + -60t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(25 + 18t + -60t2)' equal to zero and attempt to solve:

Simplifying
25 + 18t + -60t2 = 0

Solving
25 + 18t + -60t2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
-0.4166666667 + -0.3t + t2 = 0.0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -0.3t + 0.4166666667 + t2 = 0.0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -0.3t + t2 = 0.0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -0.3t + t2 = 0.0 + 0.4166666667
-0.3t + t2 = 0.0 + 0.4166666667

Combine like terms: 0.0 + 0.4166666667 = 0.4166666667
-0.3t + t2 = 0.4166666667

The t term is -0.3t.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3t + 0.0225 + t2 = 0.4166666667 + 0.0225

Reorder the terms:
0.0225 + -0.3t + t2 = 0.4166666667 + 0.0225

Combine like terms: 0.4166666667 + 0.0225 = 0.4391666667
0.0225 + -0.3t + t2 = 0.4391666667

Factor a perfect square on the left side:
(t + -0.15)(t + -0.15) = 0.4391666667

Calculate the square root of the right side: 0.662696512

Break this problem into two subproblems by setting 
(t + -0.15) equal to 0.662696512 and -0.662696512.

Subproblem 1
t + -0.15 = 0.662696512

Simplifying
t + -0.15 = 0.662696512

Reorder the terms:
-0.15 + t = 0.662696512

Solving
-0.15 + t = 0.662696512

Solving for variable 't'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + t = 0.662696512 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + t = 0.662696512 + 0.15
t = 0.662696512 + 0.15

Combine like terms: 0.662696512 + 0.15 = 0.812696512
t = 0.812696512

Simplifying
t = 0.812696512

Subproblem 2
t + -0.15 = -0.662696512

Simplifying
t + -0.15 = -0.662696512

Reorder the terms:
-0.15 + t = -0.662696512

Solving
-0.15 + t = -0.662696512

Solving for variable 't'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + t = -0.662696512 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + t = -0.662696512 + 0.15
t = -0.662696512 + 0.15

Combine like terms: -0.662696512 + 0.15 = -0.512696512
t = -0.512696512

Simplifying
t = -0.512696512

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.812696512, -0.512696512}
Solution
t = {0.812696512, -0.512696512}