(4+5)4=(x+4+x-2)x-2

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

Simplifying
(4 + 5) * 4 = (x + 4 + x + -2) * x + -2

Combine like terms: 4 + 5 = 9
(9) * 4 = (x + 4 + x + -2) * x + -2

Multiply 9 * 4
36 = (x + 4 + x + -2) * x + -2

Reorder the terms:
36 = (4 + -2 + x + x) * x + -2

Combine like terms: 4 + -2 = 2
36 = (2 + x + x) * x + -2

Combine like terms: x + x = 2x
36 = (2 + 2x) * x + -2

Reorder the terms for easier multiplication:
36 = x(2 + 2x) + -2
36 = (2 * x + 2x * x) + -2
36 = (2x + 2x2) + -2

Reorder the terms:
36 = -2 + 2x + 2x2

Solving
36 = -2 + 2x + 2x2

Solving for variable 'x'.

Combine like terms: 36 + 2 = 38
38 + -2x + -2x2 = -2 + 2x + 2x2 + 2 + -2x + -2x2

Reorder the terms:
38 + -2x + -2x2 = -2 + 2 + 2x + -2x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
38 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
38 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
38 + -2x + -2x2 = 0 + 2x2 + -2x2
38 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
38 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(19 + -1x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(19 + -1x + -1x2)' equal to zero and attempt to solve:

Simplifying
19 + -1x + -1x2 = 0

Solving
19 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-19 + x + x2 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + x + x2 = 0 + 19
x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
x + x2 = 19

The x term is x.  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.
 + 0.25 + x2 = 19 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 19 + 0.25

Combine like terms: 19 + 0.25 = 19.25
1.25 + x2 = 19.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
x + 0.5 = 4.387482194

Simplifying
x + 0.5 = 4.387482194

Reorder the terms:
0.5 + x = 4.387482194

Solving
0.5 + x = 4.387482194

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.387482194 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.387482194 + -0.5
x = 4.387482194 + -0.5

Combine like terms: 4.387482194 + -0.5 = 3.887482194
x = 3.887482194

Simplifying
x = 3.887482194

Subproblem 2
x + 0.5 = -4.387482194

Simplifying
x + 0.5 = -4.387482194

Reorder the terms:
0.5 + x = -4.387482194

Solving
0.5 + x = -4.387482194

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.387482194 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.387482194 + -0.5
x = -4.387482194 + -0.5

Combine like terms: -4.387482194 + -0.5 = -4.887482194
x = -4.887482194

Simplifying
x = -4.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.887482194, -4.887482194}
Solution
x = {3.887482194, -4.887482194}