12(6t+1)-15=t(t+2)

Solution for 12(6t+1)-15=t(t+2) equation:

Simplifying
12(6t + 1) + -15 = t(t + 2)

Reorder the terms:
12(1 + 6t) + -15 = t(t + 2)
(1 * 12 + 6t * 12) + -15 = t(t + 2)
(12 + 72t) + -15 = t(t + 2)

Reorder the terms:
12 + -15 + 72t = t(t + 2)

Combine like terms: 12 + -15 = -3
-3 + 72t = t(t + 2)

Reorder the terms:
-3 + 72t = t(2 + t)
-3 + 72t = (2 * t + t * t)
-3 + 72t = (2t + t2)

Solving
-3 + 72t = 2t + t2

Solving for variable 't'.

Combine like terms: 72t + -2t = 70t
-3 + 70t + -1t2 = 2t + t2 + -2t + -1t2

Reorder the terms:
-3 + 70t + -1t2 = 2t + -2t + t2 + -1t2

Combine like terms: 2t + -2t = 0
-3 + 70t + -1t2 = 0 + t2 + -1t2
-3 + 70t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-3 + 70t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -70t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -70t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -70t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -70t + t2 = 0 + -3
-70t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-70t + t2 = -3

The t term is -70t.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70t + 1225 + t2 = -3 + 1225

Reorder the terms:
1225 + -70t + t2 = -3 + 1225

Combine like terms: -3 + 1225 = 1222
1225 + -70t + t2 = 1222

Factor a perfect square on the left side:
(t + -35)(t + -35) = 1222

Calculate the square root of the right side: 34.957116586

Break this problem into two subproblems by setting 
(t + -35) equal to 34.957116586 and -34.957116586.

Subproblem 1
t + -35 = 34.957116586

Simplifying
t + -35 = 34.957116586

Reorder the terms:
-35 + t = 34.957116586

Solving
-35 + t = 34.957116586

Solving for variable 't'.

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

Add '35' to each side of the equation.
-35 + 35 + t = 34.957116586 + 35

Combine like terms: -35 + 35 = 0
0 + t = 34.957116586 + 35
t = 34.957116586 + 35

Combine like terms: 34.957116586 + 35 = 69.957116586
t = 69.957116586

Simplifying
t = 69.957116586

Subproblem 2
t + -35 = -34.957116586

Simplifying
t + -35 = -34.957116586

Reorder the terms:
-35 + t = -34.957116586

Solving
-35 + t = -34.957116586

Solving for variable 't'.

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

Add '35' to each side of the equation.
-35 + 35 + t = -34.957116586 + 35

Combine like terms: -35 + 35 = 0
0 + t = -34.957116586 + 35
t = -34.957116586 + 35

Combine like terms: -34.957116586 + 35 = 0.042883414
t = 0.042883414

Simplifying
t = 0.042883414

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {69.957116586, 0.042883414}