4(1.5c+6)2c=9

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Solution for 4(1.5c+6)2c=9 equation:


Simplifying
4(1.5c + 6) * 2c = 9

Reorder the terms:
4(6 + 1.5c) * 2c = 9

Reorder the terms for easier multiplication:
4 * 2c(6 + 1.5c) = 9

Multiply 4 * 2
8c(6 + 1.5c) = 9
(6 * 8c + 1.5c * 8c) = 9
(48c + 12c2) = 9

Solving
48c + 12c2 = 9

Solving for variable 'c'.

Reorder the terms:
-9 + 48c + 12c2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 48c + 12c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 16c + 4c2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + 16c + 4c2)' equal to zero and attempt to solve:

Simplifying
-3 + 16c + 4c2 = 0

Solving
-3 + 16c + 4c2 = 0

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

Divide each side by '4'.
-0.75 + 4c + c2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 4c + 0.75 + c2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 4c + c2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 4c + c2 = 0 + 0.75
4c + c2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
4c + c2 = 0.75

The c term is 4c.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4c + 4 + c2 = 0.75 + 4

Reorder the terms:
4 + 4c + c2 = 0.75 + 4

Combine like terms: 0.75 + 4 = 4.75
4 + 4c + c2 = 4.75

Factor a perfect square on the left side:
(c + 2)(c + 2) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(c + 2) equal to 2.179449472 and -2.179449472.


Subproblem 1
c + 2 = 2.179449472

Simplifying
c + 2 = 2.179449472

Reorder the terms:
2 + c = 2.179449472

Solving
2 + c = 2.179449472

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = 2.179449472 + -2

Combine like terms: 2 + -2 = 0
0 + c = 2.179449472 + -2
c = 2.179449472 + -2

Combine like terms: 2.179449472 + -2 = 0.179449472
c = 0.179449472

Simplifying
c = 0.179449472


Subproblem 2
c + 2 = -2.179449472

Simplifying
c + 2 = -2.179449472

Reorder the terms:
2 + c = -2.179449472

Solving
2 + c = -2.179449472

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = -2.179449472 + -2

Combine like terms: 2 + -2 = 0
0 + c = -2.179449472 + -2
c = -2.179449472 + -2

Combine like terms: -2.179449472 + -2 = -4.179449472
c = -4.179449472

Simplifying
c = -4.179449472


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.179449472, -4.179449472}
Solution
c = {0.179449472, -4.179449472}

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