7(c-1)c=6

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Solution for 7(c-1)c=6 equation:


Simplifying
7(c + -1) * c = 6

Reorder the terms:
7(-1 + c) * c = 6

Reorder the terms for easier multiplication:
7c(-1 + c) = 6
(-1 * 7c + c * 7c) = 6
(-7c + 7c2) = 6

Solving
-7c + 7c2 = 6

Solving for variable 'c'.

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

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

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

Divide each side by '7'.
-0.8571428571 + -1c + c2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -1c + 0.8571428571 + c2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -1c + c2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -1c + c2 = 0 + 0.8571428571
-1c + c2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-1c + c2 = 0.8571428571

The c term is -1c.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1c + 0.25 + c2 = 0.8571428571 + 0.25

Reorder the terms:
0.25 + -1c + c2 = 0.8571428571 + 0.25

Combine like terms: 0.8571428571 + 0.25 = 1.1071428571
0.25 + -1c + c2 = 1.1071428571

Factor a perfect square on the left side:
(c + -0.5)(c + -0.5) = 1.1071428571

Calculate the square root of the right side: 1.052208562

Break this problem into two subproblems by setting 
(c + -0.5) equal to 1.052208562 and -1.052208562.

Subproblem 1

c + -0.5 = 1.052208562 Simplifying c + -0.5 = 1.052208562 Reorder the terms: -0.5 + c = 1.052208562 Solving -0.5 + c = 1.052208562 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = 1.052208562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 1.052208562 + 0.5 c = 1.052208562 + 0.5 Combine like terms: 1.052208562 + 0.5 = 1.552208562 c = 1.552208562 Simplifying c = 1.552208562

Subproblem 2

c + -0.5 = -1.052208562 Simplifying c + -0.5 = -1.052208562 Reorder the terms: -0.5 + c = -1.052208562 Solving -0.5 + c = -1.052208562 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = -1.052208562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -1.052208562 + 0.5 c = -1.052208562 + 0.5 Combine like terms: -1.052208562 + 0.5 = -0.552208562 c = -0.552208562 Simplifying c = -0.552208562

Solution

The solution to the problem is based on the solutions from the subproblems. c = {1.552208562, -0.552208562}

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