(6t+4)(6t+4)=6

Solution for (6t+4)(6t+4)=6 equation:

Simplifying
(6t + 4)(6t + 4) = 6

Reorder the terms:
(4 + 6t)(6t + 4) = 6

Reorder the terms:
(4 + 6t)(4 + 6t) = 6

Multiply (4 + 6t) * (4 + 6t)
(4(4 + 6t) + 6t * (4 + 6t)) = 6
((4 * 4 + 6t * 4) + 6t * (4 + 6t)) = 6
((16 + 24t) + 6t * (4 + 6t)) = 6
(16 + 24t + (4 * 6t + 6t * 6t)) = 6
(16 + 24t + (24t + 36t2)) = 6

Combine like terms: 24t + 24t = 48t
(16 + 48t + 36t2) = 6

Solving
16 + 48t + 36t2 = 6

Solving for variable 't'.

Reorder the terms:
16 + -6 + 48t + 36t2 = 6 + -6

Combine like terms: 16 + -6 = 10
10 + 48t + 36t2 = 6 + -6

Combine like terms: 6 + -6 = 0
10 + 48t + 36t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 24t + 18t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 24t + 18t2)' equal to zero and attempt to solve:

Simplifying
5 + 24t + 18t2 = 0

Solving
5 + 24t + 18t2 = 0

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

Divide each side by '18'.
0.2777777778 + 1.333333333t + t2 = 0

Move the constant term to the right:

Add '-0.2777777778' to each side of the equation.
0.2777777778 + 1.333333333t + -0.2777777778 + t2 = 0 + -0.2777777778

Reorder the terms:
0.2777777778 + -0.2777777778 + 1.333333333t + t2 = 0 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + 1.333333333t + t2 = 0 + -0.2777777778
1.333333333t + t2 = 0 + -0.2777777778

Combine like terms: 0 + -0.2777777778 = -0.2777777778
1.333333333t + t2 = -0.2777777778

The t term is 1.333333333t.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333t + 0.4444444442 + t2 = -0.2777777778 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333t + t2 = -0.2777777778 + 0.4444444442

Combine like terms: -0.2777777778 + 0.4444444442 = 0.1666666664
0.4444444442 + 1.333333333t + t2 = 0.1666666664

Factor a perfect square on the left side:
(t + 0.6666666665)(t + 0.6666666665) = 0.1666666664

Calculate the square root of the right side: 0.40824829

Break this problem into two subproblems by setting 
(t + 0.6666666665) equal to 0.40824829 and -0.40824829.

Subproblem 1
t + 0.6666666665 = 0.40824829

Simplifying
t + 0.6666666665 = 0.40824829

Reorder the terms:
0.6666666665 + t = 0.40824829

Solving
0.6666666665 + t = 0.40824829

Solving for variable 't'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + t = 0.40824829 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + t = 0.40824829 + -0.6666666665
t = 0.40824829 + -0.6666666665

Combine like terms: 0.40824829 + -0.6666666665 = -0.2584183765
t = -0.2584183765

Simplifying
t = -0.2584183765

Subproblem 2
t + 0.6666666665 = -0.40824829

Simplifying
t + 0.6666666665 = -0.40824829

Reorder the terms:
0.6666666665 + t = -0.40824829

Solving
0.6666666665 + t = -0.40824829

Solving for variable 't'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + t = -0.40824829 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + t = -0.40824829 + -0.6666666665
t = -0.40824829 + -0.6666666665

Combine like terms: -0.40824829 + -0.6666666665 = -1.0749149565
t = -1.0749149565

Simplifying
t = -1.0749149565

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.2584183765, -1.0749149565}
Solution
t = {-0.2584183765, -1.0749149565}