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

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

Simplifying
(x + 7)(2x + -3) + 2x = 0

Reorder the terms:
(7 + x)(2x + -3) + 2x = 0

Reorder the terms:
(7 + x)(-3 + 2x) + 2x = 0

Multiply (7 + x) * (-3 + 2x)
(7(-3 + 2x) + x(-3 + 2x)) + 2x = 0
((-3 * 7 + 2x * 7) + x(-3 + 2x)) + 2x = 0
((-21 + 14x) + x(-3 + 2x)) + 2x = 0
(-21 + 14x + (-3 * x + 2x * x)) + 2x = 0
(-21 + 14x + (-3x + 2x2)) + 2x = 0

Combine like terms: 14x + -3x = 11x
(-21 + 11x + 2x2) + 2x = 0

Reorder the terms:
-21 + 11x + 2x + 2x2 = 0

Combine like terms: 11x + 2x = 13x
-21 + 13x + 2x2 = 0

Solving
-21 + 13x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-10.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + 6.5x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + 6.5x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + 6.5x + x2 = 0 + 10.5
6.5x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
6.5x + x2 = 10.5

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 = 10.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 10.5 + 10.5625

Combine like terms: 10.5 + 10.5625 = 21.0625
10.5625 + 6.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + 3.25) equal to 4.589389938 and -4.589389938.

Subproblem 1
x + 3.25 = 4.589389938

Simplifying
x + 3.25 = 4.589389938

Reorder the terms:
3.25 + x = 4.589389938

Solving
3.25 + x = 4.589389938

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 = 4.589389938 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 4.589389938 + -3.25
x = 4.589389938 + -3.25

Combine like terms: 4.589389938 + -3.25 = 1.339389938
x = 1.339389938

Simplifying
x = 1.339389938

Subproblem 2
x + 3.25 = -4.589389938

Simplifying
x + 3.25 = -4.589389938

Reorder the terms:
3.25 + x = -4.589389938

Solving
3.25 + x = -4.589389938

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 = -4.589389938 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -4.589389938 + -3.25
x = -4.589389938 + -3.25

Combine like terms: -4.589389938 + -3.25 = -7.839389938
x = -7.839389938

Simplifying
x = -7.839389938

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.339389938, -7.839389938}