4(1.5c+6)2c=-9

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 = 3.25
4 + 4c + c2 = 3.25

Factor a perfect square on the left side:
(c + 2)(c + 2) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(c + 2) equal to 1.802775638 and -1.802775638.

Subproblem 1
c + 2 = 1.802775638

Simplifying
c + 2 = 1.802775638

Reorder the terms:
2 + c = 1.802775638

Solving
2 + c = 1.802775638

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 = 1.802775638 + -2

Combine like terms: 2 + -2 = 0
0 + c = 1.802775638 + -2
c = 1.802775638 + -2

Combine like terms: 1.802775638 + -2 = -0.197224362
c = -0.197224362

Simplifying
c = -0.197224362

Subproblem 2
c + 2 = -1.802775638

Simplifying
c + 2 = -1.802775638

Reorder the terms:
2 + c = -1.802775638

Solving
2 + c = -1.802775638

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 = -1.802775638 + -2

Combine like terms: 2 + -2 = 0
0 + c = -1.802775638 + -2
c = -1.802775638 + -2

Combine like terms: -1.802775638 + -2 = -3.802775638
c = -3.802775638

Simplifying
c = -3.802775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.197224362, -3.802775638}
Solution
c = {-0.197224362, -3.802775638}