22x(3+4x)=3x(3+2)-4

Solution for 22x(3+4x)=3x(3+2)-4 equation:

Simplifying
22x(3 + 4x) = 3x(3 + 2) + -4
(3 * 22x + 4x * 22x) = 3x(3 + 2) + -4
(66x + 88x2) = 3x(3 + 2) + -4

Combine like terms: 3 + 2 = 5
66x + 88x2 = 3x(5) + -4

Reorder the terms for easier multiplication:
66x + 88x2 = 3 * 5x + -4

Multiply 3 * 5
66x + 88x2 = 15x + -4

Reorder the terms:
66x + 88x2 = -4 + 15x

Solving
66x + 88x2 = -4 + 15x

Solving for variable 'x'.

Reorder the terms:
4 + 66x + -15x + 88x2 = -4 + 15x + 4 + -15x

Combine like terms: 66x + -15x = 51x
4 + 51x + 88x2 = -4 + 15x + 4 + -15x

Reorder the terms:
4 + 51x + 88x2 = -4 + 4 + 15x + -15x

Combine like terms: -4 + 4 = 0
4 + 51x + 88x2 = 0 + 15x + -15x
4 + 51x + 88x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
4 + 51x + 88x2 = 0

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

Divide each side by '88'.
0.04545454545 + 0.5795454545x + x2 = 0

Move the constant term to the right:

Add '-0.04545454545' to each side of the equation.
0.04545454545 + 0.5795454545x + -0.04545454545 + x2 = 0 + -0.04545454545

Reorder the terms:
0.04545454545 + -0.04545454545 + 0.5795454545x + x2 = 0 + -0.04545454545

Combine like terms: 0.04545454545 + -0.04545454545 = 0.00000000000
0.00000000000 + 0.5795454545x + x2 = 0 + -0.04545454545
0.5795454545x + x2 = 0 + -0.04545454545

Combine like terms: 0 + -0.04545454545 = -0.04545454545
0.5795454545x + x2 = -0.04545454545

The x term is 0.5795454545x.  Take half its coefficient (0.2897727273).
Square it (0.08396823349) and add it to both sides.

Add '0.08396823349' to each side of the equation.
0.5795454545x + 0.08396823349 + x2 = -0.04545454545 + 0.08396823349

Reorder the terms:
0.08396823349 + 0.5795454545x + x2 = -0.04545454545 + 0.08396823349

Combine like terms: -0.04545454545 + 0.08396823349 = 0.03851368804
0.08396823349 + 0.5795454545x + x2 = 0.03851368804

Factor a perfect square on the left side:
(x + 0.2897727273)(x + 0.2897727273) = 0.03851368804

Calculate the square root of the right side: 0.196249046

Break this problem into two subproblems by setting 
(x + 0.2897727273) equal to 0.196249046 and -0.196249046.

Subproblem 1
x + 0.2897727273 = 0.196249046

Simplifying
x + 0.2897727273 = 0.196249046

Reorder the terms:
0.2897727273 + x = 0.196249046

Solving
0.2897727273 + x = 0.196249046

Solving for variable 'x'.

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

Add '-0.2897727273' to each side of the equation.
0.2897727273 + -0.2897727273 + x = 0.196249046 + -0.2897727273

Combine like terms: 0.2897727273 + -0.2897727273 = 0.0000000000
0.0000000000 + x = 0.196249046 + -0.2897727273
x = 0.196249046 + -0.2897727273

Combine like terms: 0.196249046 + -0.2897727273 = -0.0935236813
x = -0.0935236813

Simplifying
x = -0.0935236813

Subproblem 2
x + 0.2897727273 = -0.196249046

Simplifying
x + 0.2897727273 = -0.196249046

Reorder the terms:
0.2897727273 + x = -0.196249046

Solving
0.2897727273 + x = -0.196249046

Solving for variable 'x'.

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

Add '-0.2897727273' to each side of the equation.
0.2897727273 + -0.2897727273 + x = -0.196249046 + -0.2897727273

Combine like terms: 0.2897727273 + -0.2897727273 = 0.0000000000
0.0000000000 + x = -0.196249046 + -0.2897727273
x = -0.196249046 + -0.2897727273

Combine like terms: -0.196249046 + -0.2897727273 = -0.4860217733
x = -0.4860217733

Simplifying
x = -0.4860217733

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0935236813, -0.4860217733}