(c+3)*(4c+5)=26

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Solution for (c+3)*(4c+5)=26 equation:


Simplifying
(c + 3)(4c + 5) = 26

Reorder the terms:
(3 + c)(4c + 5) = 26

Reorder the terms:
(3 + c)(5 + 4c) = 26

Multiply (3 + c) * (5 + 4c)
(3(5 + 4c) + c(5 + 4c)) = 26
((5 * 3 + 4c * 3) + c(5 + 4c)) = 26
((15 + 12c) + c(5 + 4c)) = 26
(15 + 12c + (5 * c + 4c * c)) = 26
(15 + 12c + (5c + 4c2)) = 26

Combine like terms: 12c + 5c = 17c
(15 + 17c + 4c2) = 26

Solving
15 + 17c + 4c2 = 26

Solving for variable 'c'.

Reorder the terms:
15 + -26 + 17c + 4c2 = 26 + -26

Combine like terms: 15 + -26 = -11
-11 + 17c + 4c2 = 26 + -26

Combine like terms: 26 + -26 = 0
-11 + 17c + 4c2 = 0

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

Divide each side by '4'.
-2.75 + 4.25c + c2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 4.25c + 2.75 + c2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 4.25c + c2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 4.25c + c2 = 0 + 2.75
4.25c + c2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
4.25c + c2 = 2.75

The c term is 4.25c.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25c + 4.515625 + c2 = 2.75 + 4.515625

Reorder the terms:
4.515625 + 4.25c + c2 = 2.75 + 4.515625

Combine like terms: 2.75 + 4.515625 = 7.265625
4.515625 + 4.25c + c2 = 7.265625

Factor a perfect square on the left side:
(c + 2.125)(c + 2.125) = 7.265625

Calculate the square root of the right side: 2.695482332

Break this problem into two subproblems by setting 
(c + 2.125) equal to 2.695482332 and -2.695482332.

Subproblem 1

c + 2.125 = 2.695482332 Simplifying c + 2.125 = 2.695482332 Reorder the terms: 2.125 + c = 2.695482332 Solving 2.125 + c = 2.695482332 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + c = 2.695482332 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + c = 2.695482332 + -2.125 c = 2.695482332 + -2.125 Combine like terms: 2.695482332 + -2.125 = 0.570482332 c = 0.570482332 Simplifying c = 0.570482332

Subproblem 2

c + 2.125 = -2.695482332 Simplifying c + 2.125 = -2.695482332 Reorder the terms: 2.125 + c = -2.695482332 Solving 2.125 + c = -2.695482332 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + c = -2.695482332 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + c = -2.695482332 + -2.125 c = -2.695482332 + -2.125 Combine like terms: -2.695482332 + -2.125 = -4.820482332 c = -4.820482332 Simplifying c = -4.820482332

Solution

The solution to the problem is based on the solutions from the subproblems. c = {0.570482332, -4.820482332}

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