4(c+9)8(c-10)=120

Solution for 4(c+9)8(c-10)=120 equation:

Simplifying
4(c + 9) * 8(c + -10) = 120

Reorder the terms:
4(9 + c) * 8(c + -10) = 120

Reorder the terms:
4(9 + c) * 8(-10 + c) = 120

Reorder the terms for easier multiplication:
4 * 8(9 + c)(-10 + c) = 120

Multiply 4 * 8
32(9 + c)(-10 + c) = 120

Multiply (9 + c) * (-10 + c)
32(9(-10 + c) + c(-10 + c)) = 120
32((-10 * 9 + c * 9) + c(-10 + c)) = 120
32((-90 + 9c) + c(-10 + c)) = 120
32(-90 + 9c + (-10 * c + c * c)) = 120
32(-90 + 9c + (-10c + c2)) = 120

Combine like terms: 9c + -10c = -1c
32(-90 + -1c + c2) = 120
(-90 * 32 + -1c * 32 + c2 * 32) = 120
(-2880 + -32c + 32c2) = 120

Solving
-2880 + -32c + 32c2 = 120

Solving for variable 'c'.

Reorder the terms:
-2880 + -120 + -32c + 32c2 = 120 + -120

Combine like terms: -2880 + -120 = -3000
-3000 + -32c + 32c2 = 120 + -120

Combine like terms: 120 + -120 = 0
-3000 + -32c + 32c2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-375 + -4c + 4c2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-375 + -4c + 4c2)' equal to zero and attempt to solve:

Simplifying
-375 + -4c + 4c2 = 0

Solving
-375 + -4c + 4c2 = 0

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

Divide each side by '4'.
-93.75 + -1c + c2 = 0

Move the constant term to the right:

Add '93.75' to each side of the equation.
-93.75 + -1c + 93.75 + c2 = 0 + 93.75

Reorder the terms:
-93.75 + 93.75 + -1c + c2 = 0 + 93.75

Combine like terms: -93.75 + 93.75 = 0.00
0.00 + -1c + c2 = 0 + 93.75
-1c + c2 = 0 + 93.75

Combine like terms: 0 + 93.75 = 93.75
-1c + c2 = 93.75

The c term is -1c.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1c + 0.25 + c2 = 93.75 + 0.25

Reorder the terms:
0.25 + -1c + c2 = 93.75 + 0.25

Combine like terms: 93.75 + 0.25 = 94
0.25 + -1c + c2 = 94

Factor a perfect square on the left side:
(c + -0.5)(c + -0.5) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(c + -0.5) equal to 9.695359715 and -9.695359715.

Subproblem 1
c + -0.5 = 9.695359715

Simplifying
c + -0.5 = 9.695359715

Reorder the terms:
-0.5 + c = 9.695359715

Solving
-0.5 + c = 9.695359715

Solving for variable 'c'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + c = 9.695359715 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + c = 9.695359715 + 0.5
c = 9.695359715 + 0.5

Combine like terms: 9.695359715 + 0.5 = 10.195359715
c = 10.195359715

Simplifying
c = 10.195359715

Subproblem 2
c + -0.5 = -9.695359715

Simplifying
c + -0.5 = -9.695359715

Reorder the terms:
-0.5 + c = -9.695359715

Solving
-0.5 + c = -9.695359715

Solving for variable 'c'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + c = -9.695359715 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + c = -9.695359715 + 0.5
c = -9.695359715 + 0.5

Combine like terms: -9.695359715 + 0.5 = -9.195359715
c = -9.195359715

Simplifying
c = -9.195359715

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {10.195359715, -9.195359715}
Solution
c = {10.195359715, -9.195359715}