4c^2=-5c+3c^2-2

Solution for 4c^2=-5c+3c^2-2 equation:

Simplifying
4c2 = -5c + 3c2 + -2

Reorder the terms:
4c2 = -2 + -5c + 3c2

Solving
4c2 = -2 + -5c + 3c2

Solving for variable 'c'.

Reorder the terms:
2 + 5c + 4c2 + -3c2 = -2 + -5c + 3c2 + 2 + 5c + -3c2

Combine like terms: 4c2 + -3c2 = 1c2
2 + 5c + 1c2 = -2 + -5c + 3c2 + 2 + 5c + -3c2

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5c + -2 + c2 = 0 + -2

Reorder the terms:
2 + -2 + 5c + c2 = 0 + -2

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

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

The c term is 5c.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5c + 6.25 + c2 = -2 + 6.25

Reorder the terms:
6.25 + 5c + c2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5c + c2 = 4.25

Factor a perfect square on the left side:
(c + 2.5)(c + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(c + 2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
c + 2.5 = 2.061552813

Simplifying
c + 2.5 = 2.061552813

Reorder the terms:
2.5 + c = 2.061552813

Solving
2.5 + c = 2.061552813

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = 2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = 2.061552813 + -2.5
c = 2.061552813 + -2.5

Combine like terms: 2.061552813 + -2.5 = -0.438447187
c = -0.438447187

Simplifying
c = -0.438447187

Subproblem 2
c + 2.5 = -2.061552813

Simplifying
c + 2.5 = -2.061552813

Reorder the terms:
2.5 + c = -2.061552813

Solving
2.5 + c = -2.061552813

Solving for variable 'c'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + c = -2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + c = -2.061552813 + -2.5
c = -2.061552813 + -2.5

Combine like terms: -2.061552813 + -2.5 = -4.561552813
c = -4.561552813

Simplifying
c = -4.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.438447187, -4.561552813}