-7(t-3)4t=3(7+t)

Solution for -7(t-3)4t=3(7+t) equation:

Simplifying
-7(t + -3) * 4t = 3(7 + t)

Reorder the terms:
-7(-3 + t) * 4t = 3(7 + t)

Reorder the terms for easier multiplication:
-7 * 4t(-3 + t) = 3(7 + t)

Multiply -7 * 4
-28t(-3 + t) = 3(7 + t)
(-3 * -28t + t * -28t) = 3(7 + t)
(84t + -28t2) = 3(7 + t)
84t + -28t2 = (7 * 3 + t * 3)
84t + -28t2 = (21 + 3t)

Solving
84t + -28t2 = 21 + 3t

Solving for variable 't'.

Reorder the terms:
-21 + 84t + -3t + -28t2 = 21 + 3t + -21 + -3t

Combine like terms: 84t + -3t = 81t
-21 + 81t + -28t2 = 21 + 3t + -21 + -3t

Reorder the terms:
-21 + 81t + -28t2 = 21 + -21 + 3t + -3t

Combine like terms: 21 + -21 = 0
-21 + 81t + -28t2 = 0 + 3t + -3t
-21 + 81t + -28t2 = 3t + -3t

Combine like terms: 3t + -3t = 0
-21 + 81t + -28t2 = 0

Begin completing the square.  Divide all terms by
-28 the coefficient of the squared term: 

Divide each side by '-28'.
0.75 + -2.892857143t + t2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2.892857143t + -0.75 + t2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2.892857143t + t2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2.892857143t + t2 = 0 + -0.75
-2.892857143t + t2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2.892857143t + t2 = -0.75

The t term is -2.892857143t.  Take half its coefficient (-1.446428572).
Square it (2.092155614) and add it to both sides.

Add '2.092155614' to each side of the equation.
-2.892857143t + 2.092155614 + t2 = -0.75 + 2.092155614

Reorder the terms:
2.092155614 + -2.892857143t + t2 = -0.75 + 2.092155614

Combine like terms: -0.75 + 2.092155614 = 1.342155614
2.092155614 + -2.892857143t + t2 = 1.342155614

Factor a perfect square on the left side:
(t + -1.446428572)(t + -1.446428572) = 1.342155614

Calculate the square root of the right side: 1.1585144

Break this problem into two subproblems by setting 
(t + -1.446428572) equal to 1.1585144 and -1.1585144.

Subproblem 1
t + -1.446428572 = 1.1585144

Simplifying
t + -1.446428572 = 1.1585144

Reorder the terms:
-1.446428572 + t = 1.1585144

Solving
-1.446428572 + t = 1.1585144

Solving for variable 't'.

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

Add '1.446428572' to each side of the equation.
-1.446428572 + 1.446428572 + t = 1.1585144 + 1.446428572

Combine like terms: -1.446428572 + 1.446428572 = 0.000000000
0.000000000 + t = 1.1585144 + 1.446428572
t = 1.1585144 + 1.446428572

Combine like terms: 1.1585144 + 1.446428572 = 2.604942972
t = 2.604942972

Simplifying
t = 2.604942972

Subproblem 2
t + -1.446428572 = -1.1585144

Simplifying
t + -1.446428572 = -1.1585144

Reorder the terms:
-1.446428572 + t = -1.1585144

Solving
-1.446428572 + t = -1.1585144

Solving for variable 't'.

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

Add '1.446428572' to each side of the equation.
-1.446428572 + 1.446428572 + t = -1.1585144 + 1.446428572

Combine like terms: -1.446428572 + 1.446428572 = 0.000000000
0.000000000 + t = -1.1585144 + 1.446428572
t = -1.1585144 + 1.446428572

Combine like terms: -1.1585144 + 1.446428572 = 0.287914172
t = 0.287914172

Simplifying
t = 0.287914172

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.604942972, 0.287914172}