5(x+3)2x=7(x+4)-2

Solution for 5(x+3)2x=7(x+4)-2 equation:

Simplifying
5(x + 3) * 2x = 7(x + 4) + -2

Reorder the terms:
5(3 + x) * 2x = 7(x + 4) + -2

Reorder the terms for easier multiplication:
5 * 2x(3 + x) = 7(x + 4) + -2

Multiply 5 * 2
10x(3 + x) = 7(x + 4) + -2
(3 * 10x + x * 10x) = 7(x + 4) + -2
(30x + 10x2) = 7(x + 4) + -2

Reorder the terms:
30x + 10x2 = 7(4 + x) + -2
30x + 10x2 = (4 * 7 + x * 7) + -2
30x + 10x2 = (28 + 7x) + -2

Reorder the terms:
30x + 10x2 = 28 + -2 + 7x

Combine like terms: 28 + -2 = 26
30x + 10x2 = 26 + 7x

Solving
30x + 10x2 = 26 + 7x

Solving for variable 'x'.

Reorder the terms:
-26 + 30x + -7x + 10x2 = 26 + 7x + -26 + -7x

Combine like terms: 30x + -7x = 23x
-26 + 23x + 10x2 = 26 + 7x + -26 + -7x

Reorder the terms:
-26 + 23x + 10x2 = 26 + -26 + 7x + -7x

Combine like terms: 26 + -26 = 0
-26 + 23x + 10x2 = 0 + 7x + -7x
-26 + 23x + 10x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-26 + 23x + 10x2 = 0

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

Divide each side by '10'.
-2.6 + 2.3x + x2 = 0.0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 2.3x + 2.6 + x2 = 0.0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 2.3x + x2 = 0.0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 2.3x + x2 = 0.0 + 2.6
2.3x + x2 = 0.0 + 2.6

Combine like terms: 0.0 + 2.6 = 2.6
2.3x + x2 = 2.6

The x term is 2.3x.  Take half its coefficient (1.15).
Square it (1.3225) and add it to both sides.

Add '1.3225' to each side of the equation.
2.3x + 1.3225 + x2 = 2.6 + 1.3225

Reorder the terms:
1.3225 + 2.3x + x2 = 2.6 + 1.3225

Combine like terms: 2.6 + 1.3225 = 3.9225
1.3225 + 2.3x + x2 = 3.9225

Factor a perfect square on the left side:
(x + 1.15)(x + 1.15) = 3.9225

Calculate the square root of the right side: 1.980530232

Break this problem into two subproblems by setting 
(x + 1.15) equal to 1.980530232 and -1.980530232.

Subproblem 1
x + 1.15 = 1.980530232

Simplifying
x + 1.15 = 1.980530232

Reorder the terms:
1.15 + x = 1.980530232

Solving
1.15 + x = 1.980530232

Solving for variable 'x'.

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

Add '-1.15' to each side of the equation.
1.15 + -1.15 + x = 1.980530232 + -1.15

Combine like terms: 1.15 + -1.15 = 0.00
0.00 + x = 1.980530232 + -1.15
x = 1.980530232 + -1.15

Combine like terms: 1.980530232 + -1.15 = 0.830530232
x = 0.830530232

Simplifying
x = 0.830530232

Subproblem 2
x + 1.15 = -1.980530232

Simplifying
x + 1.15 = -1.980530232

Reorder the terms:
1.15 + x = -1.980530232

Solving
1.15 + x = -1.980530232

Solving for variable 'x'.

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

Add '-1.15' to each side of the equation.
1.15 + -1.15 + x = -1.980530232 + -1.15

Combine like terms: 1.15 + -1.15 = 0.00
0.00 + x = -1.980530232 + -1.15
x = -1.980530232 + -1.15

Combine like terms: -1.980530232 + -1.15 = -3.130530232
x = -3.130530232

Simplifying
x = -3.130530232

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.830530232, -3.130530232}