2x(x+4)=(x+3)(x-3)

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Solution for 2x(x+4)=(x+3)(x-3) equation: 


Simplifying
2x(x + 4) = (x + 3)(x + -3)

Reorder the terms:
2x(4 + x) = (x + 3)(x + -3)
(4 * 2x + x * 2x) = (x + 3)(x + -3)
(8x + 2x2) = (x + 3)(x + -3)

Reorder the terms:
8x + 2x2 = (3 + x)(x + -3)

Reorder the terms:
8x + 2x2 = (3 + x)(-3 + x)

Multiply (3 + x) * (-3 + x)
8x + 2x2 = (3(-3 + x) + x(-3 + x))
8x + 2x2 = ((-3 * 3 + x * 3) + x(-3 + x))
8x + 2x2 = ((-9 + 3x) + x(-3 + x))
8x + 2x2 = (-9 + 3x + (-3 * x + x * x))
8x + 2x2 = (-9 + 3x + (-3x + x2))

Combine like terms: 3x + -3x = 0
8x + 2x2 = (-9 + 0 + x2)
8x + 2x2 = (-9 + x2)

Solving
8x + 2x2 = -9 + x2

Solving for variable 'x'.

Reorder the terms:
9 + 8x + 2x2 + -1x2 = -9 + x2 + 9 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
9 + 8x + 1x2 = -9 + x2 + 9 + -1x2

Reorder the terms:
9 + 8x + 1x2 = -9 + 9 + x2 + -1x2

Combine like terms: -9 + 9 = 0
9 + 8x + 1x2 = 0 + x2 + -1x2
9 + 8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + 8x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 8x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 8x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8x + x2 = 0 + -9
8x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
8x + x2 = -9

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 = -9 + 16

Reorder the terms:
16 + 8x + x2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + 8x + x2 = 7

Factor a perfect square on the left side:
(x + 4)(x + 4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 4) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + 4 = 2.645751311

Simplifying
x + 4 = 2.645751311

Reorder the terms:
4 + x = 2.645751311

Solving
4 + x = 2.645751311

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 = 2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.645751311 + -4
x = 2.645751311 + -4

Combine like terms: 2.645751311 + -4 = -1.354248689
x = -1.354248689

Simplifying
x = -1.354248689


Subproblem 2
x + 4 = -2.645751311

Simplifying
x + 4 = -2.645751311

Reorder the terms:
4 + x = -2.645751311

Solving
4 + x = -2.645751311

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 = -2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.645751311 + -4
x = -2.645751311 + -4

Combine like terms: -2.645751311 + -4 = -6.645751311
x = -6.645751311

Simplifying
x = -6.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.354248689, -6.645751311}

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