4(c-3)3(2c+1)=7c+3

Solution for 4(c-3)3(2c+1)=7c+3 equation:

Simplifying
4(c + -3) * 3(2c + 1) = 7c + 3

Reorder the terms:
4(-3 + c) * 3(2c + 1) = 7c + 3

Reorder the terms:
4(-3 + c) * 3(1 + 2c) = 7c + 3

Reorder the terms for easier multiplication:
4 * 3(-3 + c)(1 + 2c) = 7c + 3

Multiply 4 * 3
12(-3 + c)(1 + 2c) = 7c + 3

Multiply (-3 + c) * (1 + 2c)
12(-3(1 + 2c) + c(1 + 2c)) = 7c + 3
12((1 * -3 + 2c * -3) + c(1 + 2c)) = 7c + 3
12((-3 + -6c) + c(1 + 2c)) = 7c + 3
12(-3 + -6c + (1 * c + 2c * c)) = 7c + 3
12(-3 + -6c + (1c + 2c2)) = 7c + 3

Combine like terms: -6c + 1c = -5c
12(-3 + -5c + 2c2) = 7c + 3
(-3 * 12 + -5c * 12 + 2c2 * 12) = 7c + 3
(-36 + -60c + 24c2) = 7c + 3

Reorder the terms:
-36 + -60c + 24c2 = 3 + 7c

Solving
-36 + -60c + 24c2 = 3 + 7c

Solving for variable 'c'.

Reorder the terms:
-36 + -3 + -60c + -7c + 24c2 = 3 + 7c + -3 + -7c

Combine like terms: -36 + -3 = -39
-39 + -60c + -7c + 24c2 = 3 + 7c + -3 + -7c

Combine like terms: -60c + -7c = -67c
-39 + -67c + 24c2 = 3 + 7c + -3 + -7c

Reorder the terms:
-39 + -67c + 24c2 = 3 + -3 + 7c + -7c

Combine like terms: 3 + -3 = 0
-39 + -67c + 24c2 = 0 + 7c + -7c
-39 + -67c + 24c2 = 7c + -7c

Combine like terms: 7c + -7c = 0
-39 + -67c + 24c2 = 0

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

Divide each side by '24'.
-1.625 + -2.791666667c + c2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + -2.791666667c + 1.625 + c2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + -2.791666667c + c2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -2.791666667c + c2 = 0 + 1.625
-2.791666667c + c2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
-2.791666667c + c2 = 1.625

The c term is -2.791666667c.  Take half its coefficient (-1.395833334).
Square it (1.948350696) and add it to both sides.

Add '1.948350696' to each side of the equation.
-2.791666667c + 1.948350696 + c2 = 1.625 + 1.948350696

Reorder the terms:
1.948350696 + -2.791666667c + c2 = 1.625 + 1.948350696

Combine like terms: 1.625 + 1.948350696 = 3.573350696
1.948350696 + -2.791666667c + c2 = 3.573350696

Factor a perfect square on the left side:
(c + -1.395833334)(c + -1.395833334) = 3.573350696

Calculate the square root of the right side: 1.890330843

Break this problem into two subproblems by setting 
(c + -1.395833334) equal to 1.890330843 and -1.890330843.

Subproblem 1
c + -1.395833334 = 1.890330843

Simplifying
c + -1.395833334 = 1.890330843

Reorder the terms:
-1.395833334 + c = 1.890330843

Solving
-1.395833334 + c = 1.890330843

Solving for variable 'c'.

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

Add '1.395833334' to each side of the equation.
-1.395833334 + 1.395833334 + c = 1.890330843 + 1.395833334

Combine like terms: -1.395833334 + 1.395833334 = 0.000000000
0.000000000 + c = 1.890330843 + 1.395833334
c = 1.890330843 + 1.395833334

Combine like terms: 1.890330843 + 1.395833334 = 3.286164177
c = 3.286164177

Simplifying
c = 3.286164177

Subproblem 2
c + -1.395833334 = -1.890330843

Simplifying
c + -1.395833334 = -1.890330843

Reorder the terms:
-1.395833334 + c = -1.890330843

Solving
-1.395833334 + c = -1.890330843

Solving for variable 'c'.

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

Add '1.395833334' to each side of the equation.
-1.395833334 + 1.395833334 + c = -1.890330843 + 1.395833334

Combine like terms: -1.395833334 + 1.395833334 = 0.000000000
0.000000000 + c = -1.890330843 + 1.395833334
c = -1.890330843 + 1.395833334

Combine like terms: -1.890330843 + 1.395833334 = -0.494497509
c = -0.494497509

Simplifying
c = -0.494497509

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.286164177, -0.494497509}