22=4(2x+5)3x

Solution for 22=4(2x+5)3x equation:

Simplifying
22 = 4(2x + 5) * 3x

Reorder the terms:
22 = 4(5 + 2x) * 3x

Reorder the terms for easier multiplication:
22 = 4 * 3x(5 + 2x)

Multiply 4 * 3
22 = 12x(5 + 2x)
22 = (5 * 12x + 2x * 12x)
22 = (60x + 24x2)

Solving
22 = 60x + 24x2

Solving for variable 'x'.

Reorder the terms:
22 + -60x + -24x2 = 60x + -60x + 24x2 + -24x2

Combine like terms: 60x + -60x = 0
22 + -60x + -24x2 = 0 + 24x2 + -24x2
22 + -60x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
22 + -60x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -30x + -12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + -30x + -12x2)' equal to zero and attempt to solve:

Simplifying
11 + -30x + -12x2 = 0

Solving
11 + -30x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.9166666667 + 2.5x + x2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + 2.5x + 0.9166666667 + x2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + 2.5x + x2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + 2.5x + x2 = 0 + 0.9166666667
2.5x + x2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
2.5x + x2 = 0.9166666667

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.9166666667 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.9166666667 + 1.5625

Combine like terms: 0.9166666667 + 1.5625 = 2.4791666667
1.5625 + 2.5x + x2 = 2.4791666667

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.4791666667

Calculate the square root of the right side: 1.574536969

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.574536969 and -1.574536969.

Subproblem 1
x + 1.25 = 1.574536969

Simplifying
x + 1.25 = 1.574536969

Reorder the terms:
1.25 + x = 1.574536969

Solving
1.25 + x = 1.574536969

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.574536969 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.574536969 + -1.25
x = 1.574536969 + -1.25

Combine like terms: 1.574536969 + -1.25 = 0.324536969
x = 0.324536969

Simplifying
x = 0.324536969

Subproblem 2
x + 1.25 = -1.574536969

Simplifying
x + 1.25 = -1.574536969

Reorder the terms:
1.25 + x = -1.574536969

Solving
1.25 + x = -1.574536969

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.574536969 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.574536969 + -1.25
x = -1.574536969 + -1.25

Combine like terms: -1.574536969 + -1.25 = -2.824536969
x = -2.824536969

Simplifying
x = -2.824536969

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.324536969, -2.824536969}
Solution
x = {0.324536969, -2.824536969}