7(-t+9)15t=-7t+6-12t

Solution for 7(-t+9)15t=-7t+6-12t equation:

Simplifying
7(-1t + 9) * 15t = -7t + 6 + -12t

Reorder the terms:
7(9 + -1t) * 15t = -7t + 6 + -12t

Reorder the terms for easier multiplication:
7 * 15t(9 + -1t) = -7t + 6 + -12t

Multiply 7 * 15
105t(9 + -1t) = -7t + 6 + -12t
(9 * 105t + -1t * 105t) = -7t + 6 + -12t
(945t + -105t2) = -7t + 6 + -12t

Reorder the terms:
945t + -105t2 = 6 + -7t + -12t

Combine like terms: -7t + -12t = -19t
945t + -105t2 = 6 + -19t

Solving
945t + -105t2 = 6 + -19t

Solving for variable 't'.

Reorder the terms:
-6 + 945t + 19t + -105t2 = 6 + -19t + -6 + 19t

Combine like terms: 945t + 19t = 964t
-6 + 964t + -105t2 = 6 + -19t + -6 + 19t

Reorder the terms:
-6 + 964t + -105t2 = 6 + -6 + -19t + 19t

Combine like terms: 6 + -6 = 0
-6 + 964t + -105t2 = 0 + -19t + 19t
-6 + 964t + -105t2 = -19t + 19t

Combine like terms: -19t + 19t = 0
-6 + 964t + -105t2 = 0

Begin completing the square.  Divide all terms by
-105 the coefficient of the squared term: 

Divide each side by '-105'.
0.05714285714 + -9.180952381t + t2 = 0

Move the constant term to the right:

Add '-0.05714285714' to each side of the equation.
0.05714285714 + -9.180952381t + -0.05714285714 + t2 = 0 + -0.05714285714

Reorder the terms:
0.05714285714 + -0.05714285714 + -9.180952381t + t2 = 0 + -0.05714285714

Combine like terms: 0.05714285714 + -0.05714285714 = 0.00000000000
0.00000000000 + -9.180952381t + t2 = 0 + -0.05714285714
-9.180952381t + t2 = 0 + -0.05714285714

Combine like terms: 0 + -0.05714285714 = -0.05714285714
-9.180952381t + t2 = -0.05714285714

The t term is -9.180952381t.  Take half its coefficient (-4.590476191).
Square it (21.07247166) and add it to both sides.

Add '21.07247166' to each side of the equation.
-9.180952381t + 21.07247166 + t2 = -0.05714285714 + 21.07247166

Reorder the terms:
21.07247166 + -9.180952381t + t2 = -0.05714285714 + 21.07247166

Combine like terms: -0.05714285714 + 21.07247166 = 21.01532880286
21.07247166 + -9.180952381t + t2 = 21.01532880286

Factor a perfect square on the left side:
(t + -4.590476191)(t + -4.590476191) = 21.01532880286

Calculate the square root of the right side: 4.584247899

Break this problem into two subproblems by setting 
(t + -4.590476191) equal to 4.584247899 and -4.584247899.

Subproblem 1
t + -4.590476191 = 4.584247899

Simplifying
t + -4.590476191 = 4.584247899

Reorder the terms:
-4.590476191 + t = 4.584247899

Solving
-4.590476191 + t = 4.584247899

Solving for variable 't'.

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

Add '4.590476191' to each side of the equation.
-4.590476191 + 4.590476191 + t = 4.584247899 + 4.590476191

Combine like terms: -4.590476191 + 4.590476191 = 0.000000000
0.000000000 + t = 4.584247899 + 4.590476191
t = 4.584247899 + 4.590476191

Combine like terms: 4.584247899 + 4.590476191 = 9.17472409
t = 9.17472409

Simplifying
t = 9.17472409

Subproblem 2
t + -4.590476191 = -4.584247899

Simplifying
t + -4.590476191 = -4.584247899

Reorder the terms:
-4.590476191 + t = -4.584247899

Solving
-4.590476191 + t = -4.584247899

Solving for variable 't'.

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

Add '4.590476191' to each side of the equation.
-4.590476191 + 4.590476191 + t = -4.584247899 + 4.590476191

Combine like terms: -4.590476191 + 4.590476191 = 0.000000000
0.000000000 + t = -4.584247899 + 4.590476191
t = -4.584247899 + 4.590476191

Combine like terms: -4.584247899 + 4.590476191 = 0.006228292
t = 0.006228292

Simplifying
t = 0.006228292

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.17472409, 0.006228292}