-x(14+2x)=13+(2x-3)

Solution for -x(14+2x)=13+(2x-3) equation:

Simplifying
-1x(14 + 2x) = 13 + (2x + -3)
(14 * -1x + 2x * -1x) = 13 + (2x + -3)
(-14x + -2x2) = 13 + (2x + -3)

Reorder the terms:
-14x + -2x2 = 13 + (-3 + 2x)

Remove parenthesis around (-3 + 2x)
-14x + -2x2 = 13 + -3 + 2x

Combine like terms: 13 + -3 = 10
-14x + -2x2 = 10 + 2x

Solving
-14x + -2x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
-10 + -14x + -2x + -2x2 = 10 + 2x + -10 + -2x

Combine like terms: -14x + -2x = -16x
-10 + -16x + -2x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-10 + -16x + -2x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-10 + -16x + -2x2 = 0 + 2x + -2x
-10 + -16x + -2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-10 + -16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5 + 8x + x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(5 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 8x + x2 = 0

Solving
5 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8x + x2 = 0 + -5
8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
8x + x2 = -5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -5 + 16

Reorder the terms:
16 + 8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + 8x + x2 = 11

Factor a perfect square on the left side:
(x + 4)(x + 4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 4) equal to 3.31662479 and -3.31662479.

Subproblem 1
x + 4 = 3.31662479

Simplifying
x + 4 = 3.31662479

Reorder the terms:
4 + x = 3.31662479

Solving
4 + x = 3.31662479

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.31662479 + -4
x = 3.31662479 + -4

Combine like terms: 3.31662479 + -4 = -0.68337521
x = -0.68337521

Simplifying
x = -0.68337521

Subproblem 2
x + 4 = -3.31662479

Simplifying
x + 4 = -3.31662479

Reorder the terms:
4 + x = -3.31662479

Solving
4 + x = -3.31662479

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.31662479 + -4
x = -3.31662479 + -4

Combine like terms: -3.31662479 + -4 = -7.31662479
x = -7.31662479

Simplifying
x = -7.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.68337521, -7.31662479}
Solution
x = {-0.68337521, -7.31662479}