5(x+2)-4x=3(x+1)9x

Solution for 5(x+2)-4x=3(x+1)9x equation:

Simplifying
5(x + 2) + -4x = 3(x + 1) * 9x

Reorder the terms:
5(2 + x) + -4x = 3(x + 1) * 9x
(2 * 5 + x * 5) + -4x = 3(x + 1) * 9x
(10 + 5x) + -4x = 3(x + 1) * 9x

Combine like terms: 5x + -4x = 1x
10 + 1x = 3(x + 1) * 9x

Reorder the terms:
10 + 1x = 3(1 + x) * 9x

Reorder the terms for easier multiplication:
10 + 1x = 3 * 9x(1 + x)

Multiply 3 * 9
10 + 1x = 27x(1 + x)
10 + 1x = (1 * 27x + x * 27x)
10 + 1x = (27x + 27x2)

Solving
10 + 1x = 27x + 27x2

Solving for variable 'x'.

Combine like terms: 1x + -27x = -26x
10 + -26x + -27x2 = 27x + 27x2 + -27x + -27x2

Reorder the terms:
10 + -26x + -27x2 = 27x + -27x + 27x2 + -27x2

Combine like terms: 27x + -27x = 0
10 + -26x + -27x2 = 0 + 27x2 + -27x2
10 + -26x + -27x2 = 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
10 + -26x + -27x2 = 0

Begin completing the square.  Divide all terms by
-27 the coefficient of the squared term: 

Divide each side by '-27'.
-0.3703703704 + 0.962962963x + x2 = 0

Move the constant term to the right:

Add '0.3703703704' to each side of the equation.
-0.3703703704 + 0.962962963x + 0.3703703704 + x2 = 0 + 0.3703703704

Reorder the terms:
-0.3703703704 + 0.3703703704 + 0.962962963x + x2 = 0 + 0.3703703704

Combine like terms: -0.3703703704 + 0.3703703704 = 0.0000000000
0.0000000000 + 0.962962963x + x2 = 0 + 0.3703703704
0.962962963x + x2 = 0 + 0.3703703704

Combine like terms: 0 + 0.3703703704 = 0.3703703704
0.962962963x + x2 = 0.3703703704

The x term is 0.962962963x.  Take half its coefficient (0.4814814815).
Square it (0.2318244170) and add it to both sides.

Add '0.2318244170' to each side of the equation.
0.962962963x + 0.2318244170 + x2 = 0.3703703704 + 0.2318244170

Reorder the terms:
0.2318244170 + 0.962962963x + x2 = 0.3703703704 + 0.2318244170

Combine like terms: 0.3703703704 + 0.2318244170 = 0.6021947874
0.2318244170 + 0.962962963x + x2 = 0.6021947874

Factor a perfect square on the left side:
(x + 0.4814814815)(x + 0.4814814815) = 0.6021947874

Calculate the square root of the right side: 0.776012105

Break this problem into two subproblems by setting 
(x + 0.4814814815) equal to 0.776012105 and -0.776012105.

Subproblem 1
x + 0.4814814815 = 0.776012105

Simplifying
x + 0.4814814815 = 0.776012105

Reorder the terms:
0.4814814815 + x = 0.776012105

Solving
0.4814814815 + x = 0.776012105

Solving for variable 'x'.

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

Add '-0.4814814815' to each side of the equation.
0.4814814815 + -0.4814814815 + x = 0.776012105 + -0.4814814815

Combine like terms: 0.4814814815 + -0.4814814815 = 0.0000000000
0.0000000000 + x = 0.776012105 + -0.4814814815
x = 0.776012105 + -0.4814814815

Combine like terms: 0.776012105 + -0.4814814815 = 0.2945306235
x = 0.2945306235

Simplifying
x = 0.2945306235

Subproblem 2
x + 0.4814814815 = -0.776012105

Simplifying
x + 0.4814814815 = -0.776012105

Reorder the terms:
0.4814814815 + x = -0.776012105

Solving
0.4814814815 + x = -0.776012105

Solving for variable 'x'.

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

Add '-0.4814814815' to each side of the equation.
0.4814814815 + -0.4814814815 + x = -0.776012105 + -0.4814814815

Combine like terms: 0.4814814815 + -0.4814814815 = 0.0000000000
0.0000000000 + x = -0.776012105 + -0.4814814815
x = -0.776012105 + -0.4814814815

Combine like terms: -0.776012105 + -0.4814814815 = -1.2574935865
x = -1.2574935865

Simplifying
x = -1.2574935865

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2945306235, -1.2574935865}