13+2c(5c-2)=29

Solution for 13+2c(5c-2)=29 equation:

Simplifying
13 + 2c(5c + -2) = 29

Reorder the terms:
13 + 2c(-2 + 5c) = 29
13 + (-2 * 2c + 5c * 2c) = 29
13 + (-4c + 10c2) = 29

Solving
13 + -4c + 10c2 = 29

Solving for variable 'c'.

Reorder the terms:
13 + -29 + -4c + 10c2 = 29 + -29

Combine like terms: 13 + -29 = -16
-16 + -4c + 10c2 = 29 + -29

Combine like terms: 29 + -29 = 0
-16 + -4c + 10c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2c + 5c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -2c + 5c2)' equal to zero and attempt to solve:

Simplifying
-8 + -2c + 5c2 = 0

Solving
-8 + -2c + 5c2 = 0

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

Divide each side by '5'.
-1.6 + -0.4c + c2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -0.4c + 1.6 + c2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -0.4c + c2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -0.4c + c2 = 0 + 1.6
-0.4c + c2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-0.4c + c2 = 1.6

The c term is -0.4c.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4c + 0.04 + c2 = 1.6 + 0.04

Reorder the terms:
0.04 + -0.4c + c2 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + -0.4c + c2 = 1.64

Factor a perfect square on the left side:
(c + -0.2)(c + -0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(c + -0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1
c + -0.2 = 1.280624847

Simplifying
c + -0.2 = 1.280624847

Reorder the terms:
-0.2 + c = 1.280624847

Solving
-0.2 + c = 1.280624847

Solving for variable 'c'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + c = 1.280624847 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + c = 1.280624847 + 0.2
c = 1.280624847 + 0.2

Combine like terms: 1.280624847 + 0.2 = 1.480624847
c = 1.480624847

Simplifying
c = 1.480624847

Subproblem 2
c + -0.2 = -1.280624847

Simplifying
c + -0.2 = -1.280624847

Reorder the terms:
-0.2 + c = -1.280624847

Solving
-0.2 + c = -1.280624847

Solving for variable 'c'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + c = -1.280624847 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + c = -1.280624847 + 0.2
c = -1.280624847 + 0.2

Combine like terms: -1.280624847 + 0.2 = -1.080624847
c = -1.080624847

Simplifying
c = -1.080624847

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.480624847, -1.080624847}
Solution
c = {1.480624847, -1.080624847}