(4t+6)(4t+6)=15

Solution for (4t+6)(4t+6)=15 equation:

Simplifying
(4t + 6)(4t + 6) = 15

Reorder the terms:
(6 + 4t)(4t + 6) = 15

Reorder the terms:
(6 + 4t)(6 + 4t) = 15

Multiply (6 + 4t) * (6 + 4t)
(6(6 + 4t) + 4t * (6 + 4t)) = 15
((6 * 6 + 4t * 6) + 4t * (6 + 4t)) = 15
((36 + 24t) + 4t * (6 + 4t)) = 15
(36 + 24t + (6 * 4t + 4t * 4t)) = 15
(36 + 24t + (24t + 16t2)) = 15

Combine like terms: 24t + 24t = 48t
(36 + 48t + 16t2) = 15

Solving
36 + 48t + 16t2 = 15

Solving for variable 't'.

Reorder the terms:
36 + -15 + 48t + 16t2 = 15 + -15

Combine like terms: 36 + -15 = 21
21 + 48t + 16t2 = 15 + -15

Combine like terms: 15 + -15 = 0
21 + 48t + 16t2 = 0

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

Divide each side by '16'.
1.3125 + 3t + t2 = 0

Move the constant term to the right:

Add '-1.3125' to each side of the equation.
1.3125 + 3t + -1.3125 + t2 = 0 + -1.3125

Reorder the terms:
1.3125 + -1.3125 + 3t + t2 = 0 + -1.3125

Combine like terms: 1.3125 + -1.3125 = 0.0000
0.0000 + 3t + t2 = 0 + -1.3125
3t + t2 = 0 + -1.3125

Combine like terms: 0 + -1.3125 = -1.3125
3t + t2 = -1.3125

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = -1.3125 + 2.25

Reorder the terms:
2.25 + 3t + t2 = -1.3125 + 2.25

Combine like terms: -1.3125 + 2.25 = 0.9375
2.25 + 3t + t2 = 0.9375

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 0.9375

Calculate the square root of the right side: 0.968245837

Break this problem into two subproblems by setting 
(t + 1.5) equal to 0.968245837 and -0.968245837.

Subproblem 1
t + 1.5 = 0.968245837

Simplifying
t + 1.5 = 0.968245837

Reorder the terms:
1.5 + t = 0.968245837

Solving
1.5 + t = 0.968245837

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 0.968245837 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 0.968245837 + -1.5
t = 0.968245837 + -1.5

Combine like terms: 0.968245837 + -1.5 = -0.531754163
t = -0.531754163

Simplifying
t = -0.531754163

Subproblem 2
t + 1.5 = -0.968245837

Simplifying
t + 1.5 = -0.968245837

Reorder the terms:
1.5 + t = -0.968245837

Solving
1.5 + t = -0.968245837

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = -0.968245837 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -0.968245837 + -1.5
t = -0.968245837 + -1.5

Combine like terms: -0.968245837 + -1.5 = -2.468245837
t = -2.468245837

Simplifying
t = -2.468245837

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.531754163, -2.468245837}