2c^2+4c-6=2

Solution for 2c^2+4c-6=2 equation:

Simplifying
2c2 + 4c + -6 = 2

Reorder the terms:
-6 + 4c + 2c2 = 2

Solving
-6 + 4c + 2c2 = 2

Solving for variable 'c'.

Reorder the terms:
-6 + -2 + 4c + 2c2 = 2 + -2

Combine like terms: -6 + -2 = -8
-8 + 4c + 2c2 = 2 + -2

Combine like terms: 2 + -2 = 0
-8 + 4c + 2c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 2c + c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 2c + c2)' equal to zero and attempt to solve:

Simplifying
-4 + 2c + c2 = 0

Solving
-4 + 2c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2c + 4 + c2 = 0 + 4

Reorder the terms:
-4 + 4 + 2c + c2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2c + c2 = 0 + 4
2c + c2 = 0 + 4

Combine like terms: 0 + 4 = 4
2c + c2 = 4

The c term is 2c.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2c + 1 + c2 = 4 + 1

Reorder the terms:
1 + 2c + c2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + 2c + c2 = 5

Factor a perfect square on the left side:
(c + 1)(c + 1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(c + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1
c + 1 = 2.236067978

Simplifying
c + 1 = 2.236067978

Reorder the terms:
1 + c = 2.236067978

Solving
1 + c = 2.236067978

Solving for variable 'c'.

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

Add '-1' to each side of the equation.
1 + -1 + c = 2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + c = 2.236067978 + -1
c = 2.236067978 + -1

Combine like terms: 2.236067978 + -1 = 1.236067978
c = 1.236067978

Simplifying
c = 1.236067978

Subproblem 2
c + 1 = -2.236067978

Simplifying
c + 1 = -2.236067978

Reorder the terms:
1 + c = -2.236067978

Solving
1 + c = -2.236067978

Solving for variable 'c'.

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

Add '-1' to each side of the equation.
1 + -1 + c = -2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + c = -2.236067978 + -1
c = -2.236067978 + -1

Combine like terms: -2.236067978 + -1 = -3.236067978
c = -3.236067978

Simplifying
c = -3.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.236067978, -3.236067978}
Solution
c = {1.236067978, -3.236067978}