7x[(x+4)-(2x+1)]=10

Solution for 7x[(x+4)-(2x+1)]=10 equation:

Simplifying
7x[(x + 4) + -1(2x + 1)] = 10

Reorder the terms:
7x[(4 + x) + -1(2x + 1)] = 10

Remove parenthesis around (4 + x)
7x[4 + x + -1(2x + 1)] = 10

Reorder the terms:
7x[4 + x + -1(1 + 2x)] = 10
7x[4 + x + (1 * -1 + 2x * -1)] = 10
7x[4 + x + (-1 + -2x)] = 10

Reorder the terms:
7x[4 + -1 + x + -2x] = 10

Combine like terms: 4 + -1 = 3
7x[3 + x + -2x] = 10

Combine like terms: x + -2x = -1x
7x[3 + -1x] = 10
[3 * 7x + -1x * 7x] = 10
[21x + -7x2] = 10

Solving
21x + -7x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 21x + -7x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 21x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
1.428571429 + -3x + x2 = 0

Move the constant term to the right:

Add '-1.428571429' to each side of the equation.
1.428571429 + -3x + -1.428571429 + x2 = 0 + -1.428571429

Reorder the terms:
1.428571429 + -1.428571429 + -3x + x2 = 0 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + -3x + x2 = 0 + -1.428571429
-3x + x2 = 0 + -1.428571429

Combine like terms: 0 + -1.428571429 = -1.428571429
-3x + x2 = -1.428571429

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -1.428571429 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -1.428571429 + 2.25

Combine like terms: -1.428571429 + 2.25 = 0.821428571
2.25 + -3x + x2 = 0.821428571

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 0.821428571

Calculate the square root of the right side: 0.906326967

Break this problem into two subproblems by setting 
(x + -1.5) equal to 0.906326967 and -0.906326967.

Subproblem 1
x + -1.5 = 0.906326967

Simplifying
x + -1.5 = 0.906326967

Reorder the terms:
-1.5 + x = 0.906326967

Solving
-1.5 + x = 0.906326967

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 0.906326967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 0.906326967 + 1.5
x = 0.906326967 + 1.5

Combine like terms: 0.906326967 + 1.5 = 2.406326967
x = 2.406326967

Simplifying
x = 2.406326967

Subproblem 2
x + -1.5 = -0.906326967

Simplifying
x + -1.5 = -0.906326967

Reorder the terms:
-1.5 + x = -0.906326967

Solving
-1.5 + x = -0.906326967

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -0.906326967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -0.906326967 + 1.5
x = -0.906326967 + 1.5

Combine like terms: -0.906326967 + 1.5 = 0.593673033
x = 0.593673033

Simplifying
x = 0.593673033

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.406326967, 0.593673033}