2c(c-3)=7

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

Simplifying
2c(c + -3) = 7

Reorder the terms:
2c(-3 + c) = 7
(-3 * 2c + c * 2c) = 7
(-6c + 2c2) = 7

Solving
-6c + 2c2 = 7

Solving for variable 'c'.

Reorder the terms:
-7 + -6c + 2c2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -6c + 2c2 = 0

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

Divide each side by '2'.
-3.5 + -3c + c2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -3c + 3.5 + c2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -3c + c2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -3c + c2 = 0 + 3.5
-3c + c2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-3c + c2 = 3.5

The c term is -3c.  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.
-3c + 2.25 + c2 = 3.5 + 2.25

Reorder the terms:
2.25 + -3c + c2 = 3.5 + 2.25

Combine like terms: 3.5 + 2.25 = 5.75
2.25 + -3c + c2 = 5.75

Factor a perfect square on the left side:
(c + -1.5)(c + -1.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(c + -1.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
c + -1.5 = 2.397915762

Simplifying
c + -1.5 = 2.397915762

Reorder the terms:
-1.5 + c = 2.397915762

Solving
-1.5 + c = 2.397915762

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = 2.397915762 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = 2.397915762 + 1.5
c = 2.397915762 + 1.5

Combine like terms: 2.397915762 + 1.5 = 3.897915762
c = 3.897915762

Simplifying
c = 3.897915762

Subproblem 2
c + -1.5 = -2.397915762

Simplifying
c + -1.5 = -2.397915762

Reorder the terms:
-1.5 + c = -2.397915762

Solving
-1.5 + c = -2.397915762

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = -2.397915762 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = -2.397915762 + 1.5
c = -2.397915762 + 1.5

Combine like terms: -2.397915762 + 1.5 = -0.897915762
c = -0.897915762

Simplifying
c = -0.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.897915762, -0.897915762}