-14+3(x+10)=7(x+4)x

Solution for -14+3(x+10)=7(x+4)x equation:

Simplifying
-14 + 3(x + 10) = 7(x + 4) * x

Reorder the terms:
-14 + 3(10 + x) = 7(x + 4) * x
-14 + (10 * 3 + x * 3) = 7(x + 4) * x
-14 + (30 + 3x) = 7(x + 4) * x

Combine like terms: -14 + 30 = 16
16 + 3x = 7(x + 4) * x

Reorder the terms:
16 + 3x = 7(4 + x) * x

Reorder the terms for easier multiplication:
16 + 3x = 7x(4 + x)
16 + 3x = (4 * 7x + x * 7x)
16 + 3x = (28x + 7x2)

Solving
16 + 3x = 28x + 7x2

Solving for variable 'x'.

Combine like terms: 3x + -28x = -25x
16 + -25x + -7x2 = 28x + 7x2 + -28x + -7x2

Reorder the terms:
16 + -25x + -7x2 = 28x + -28x + 7x2 + -7x2

Combine like terms: 28x + -28x = 0
16 + -25x + -7x2 = 0 + 7x2 + -7x2
16 + -25x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
16 + -25x + -7x2 = 0

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

Divide each side by '-7'.
-2.285714286 + 3.571428571x + x2 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + 3.571428571x + 2.285714286 + x2 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + 3.571428571x + x2 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + 3.571428571x + x2 = 0 + 2.285714286
3.571428571x + x2 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
3.571428571x + x2 = 2.285714286

The x term is 3.571428571x.  Take half its coefficient (1.785714286).
Square it (3.188775511) and add it to both sides.

Add '3.188775511' to each side of the equation.
3.571428571x + 3.188775511 + x2 = 2.285714286 + 3.188775511

Reorder the terms:
3.188775511 + 3.571428571x + x2 = 2.285714286 + 3.188775511

Combine like terms: 2.285714286 + 3.188775511 = 5.474489797
3.188775511 + 3.571428571x + x2 = 5.474489797

Factor a perfect square on the left side:
(x + 1.785714286)(x + 1.785714286) = 5.474489797

Calculate the square root of the right side: 2.339762765

Break this problem into two subproblems by setting 
(x + 1.785714286) equal to 2.339762765 and -2.339762765.

Subproblem 1
x + 1.785714286 = 2.339762765

Simplifying
x + 1.785714286 = 2.339762765

Reorder the terms:
1.785714286 + x = 2.339762765

Solving
1.785714286 + x = 2.339762765

Solving for variable 'x'.

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

Add '-1.785714286' to each side of the equation.
1.785714286 + -1.785714286 + x = 2.339762765 + -1.785714286

Combine like terms: 1.785714286 + -1.785714286 = 0.000000000
0.000000000 + x = 2.339762765 + -1.785714286
x = 2.339762765 + -1.785714286

Combine like terms: 2.339762765 + -1.785714286 = 0.554048479
x = 0.554048479

Simplifying
x = 0.554048479

Subproblem 2
x + 1.785714286 = -2.339762765

Simplifying
x + 1.785714286 = -2.339762765

Reorder the terms:
1.785714286 + x = -2.339762765

Solving
1.785714286 + x = -2.339762765

Solving for variable 'x'.

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

Add '-1.785714286' to each side of the equation.
1.785714286 + -1.785714286 + x = -2.339762765 + -1.785714286

Combine like terms: 1.785714286 + -1.785714286 = 0.000000000
0.000000000 + x = -2.339762765 + -1.785714286
x = -2.339762765 + -1.785714286

Combine like terms: -2.339762765 + -1.785714286 = -4.125477051
x = -4.125477051

Simplifying
x = -4.125477051

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.554048479, -4.125477051}