c^2-6=2c^2+3c-1

Solution for c^2-6=2c^2+3c-1 equation:

Simplifying
c2 + -6 = 2c2 + 3c + -1

Reorder the terms:
-6 + c2 = 2c2 + 3c + -1

Reorder the terms:
-6 + c2 = -1 + 3c + 2c2

Solving
-6 + c2 = -1 + 3c + 2c2

Solving for variable 'c'.

Reorder the terms:
-6 + 1 + -3c + c2 + -2c2 = -1 + 3c + 2c2 + 1 + -3c + -2c2

Combine like terms: -6 + 1 = -5
-5 + -3c + c2 + -2c2 = -1 + 3c + 2c2 + 1 + -3c + -2c2

Combine like terms: c2 + -2c2 = -1c2
-5 + -3c + -1c2 = -1 + 3c + 2c2 + 1 + -3c + -2c2

Reorder the terms:
-5 + -3c + -1c2 = -1 + 1 + 3c + -3c + 2c2 + -2c2

Combine like terms: -1 + 1 = 0
-5 + -3c + -1c2 = 0 + 3c + -3c + 2c2 + -2c2
-5 + -3c + -1c2 = 3c + -3c + 2c2 + -2c2

Combine like terms: 3c + -3c = 0
-5 + -3c + -1c2 = 0 + 2c2 + -2c2
-5 + -3c + -1c2 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
-5 + -3c + -1c2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 3c + c2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 3c + c2)' equal to zero and attempt to solve:

Simplifying
5 + 3c + c2 = 0

Solving
5 + 3c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 3c + -5 + c2 = 0 + -5

Reorder the terms:
5 + -5 + 3c + c2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3c + c2 = 0 + -5
3c + c2 = 0 + -5

Combine like terms: 0 + -5 = -5
3c + c2 = -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 = -5 + 2.25

Reorder the terms:
2.25 + 3c + c2 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + 3c + c2 = -2.75

Factor a perfect square on the left side:
(c + 1.5)(c + 1.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.