7-2x(x+4)=14+5x

Solution for 7-2x(x+4)=14+5x equation:

Simplifying
7 + -2x(x + 4) = 14 + 5x

Reorder the terms:
7 + -2x(4 + x) = 14 + 5x
7 + (4 * -2x + x * -2x) = 14 + 5x
7 + (-8x + -2x2) = 14 + 5x

Solving
7 + -8x + -2x2 = 14 + 5x

Solving for variable 'x'.

Reorder the terms:
7 + -14 + -8x + -5x + -2x2 = 14 + 5x + -14 + -5x

Combine like terms: 7 + -14 = -7
-7 + -8x + -5x + -2x2 = 14 + 5x + -14 + -5x

Combine like terms: -8x + -5x = -13x
-7 + -13x + -2x2 = 14 + 5x + -14 + -5x

Reorder the terms:
-7 + -13x + -2x2 = 14 + -14 + 5x + -5x

Combine like terms: 14 + -14 = 0
-7 + -13x + -2x2 = 0 + 5x + -5x
-7 + -13x + -2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-7 + -13x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 13x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 13x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + 13x + 2x2 = 0

Solving
7 + 13x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 6.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 6.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 6.5x + x2 = 0 + -3.5
6.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
6.5x + x2 = -3.5

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -3.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -3.5 + 10.5625

Combine like terms: -3.5 + 10.5625 = 7.0625
10.5625 + 6.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + 3.25) equal to 2.657536453 and -2.657536453.

Subproblem 1
x + 3.25 = 2.657536453

Simplifying
x + 3.25 = 2.657536453

Reorder the terms:
3.25 + x = 2.657536453

Solving
3.25 + x = 2.657536453

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 2.657536453 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 2.657536453 + -3.25
x = 2.657536453 + -3.25

Combine like terms: 2.657536453 + -3.25 = -0.592463547
x = -0.592463547

Simplifying
x = -0.592463547

Subproblem 2
x + 3.25 = -2.657536453

Simplifying
x + 3.25 = -2.657536453

Reorder the terms:
3.25 + x = -2.657536453

Solving
3.25 + x = -2.657536453

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -2.657536453 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -2.657536453 + -3.25
x = -2.657536453 + -3.25

Combine like terms: -2.657536453 + -3.25 = -5.907536453
x = -5.907536453

Simplifying
x = -5.907536453

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.592463547, -5.907536453}
Solution
x = {-0.592463547, -5.907536453}