4(x-2)(x+2)-2-3x(x+2)=0

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Solution for 4(x-2)(x+2)-2-3x(x+2)=0 equation:


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

Reorder the terms:
4(-2 + x)(x + 2) + -2 + -3x(x + 2) = 0

Reorder the terms:
4(-2 + x)(2 + x) + -2 + -3x(x + 2) = 0

Multiply (-2 + x) * (2 + x)
4(-2(2 + x) + x(2 + x)) + -2 + -3x(x + 2) = 0
4((2 * -2 + x * -2) + x(2 + x)) + -2 + -3x(x + 2) = 0
4((-4 + -2x) + x(2 + x)) + -2 + -3x(x + 2) = 0
4(-4 + -2x + (2 * x + x * x)) + -2 + -3x(x + 2) = 0
4(-4 + -2x + (2x + x2)) + -2 + -3x(x + 2) = 0

Combine like terms: -2x + 2x = 0
4(-4 + 0 + x2) + -2 + -3x(x + 2) = 0
4(-4 + x2) + -2 + -3x(x + 2) = 0
(-4 * 4 + x2 * 4) + -2 + -3x(x + 2) = 0
(-16 + 4x2) + -2 + -3x(x + 2) = 0

Reorder the terms:
-16 + 4x2 + -2 + -3x(2 + x) = 0
-16 + 4x2 + -2 + (2 * -3x + x * -3x) = 0
-16 + 4x2 + -2 + (-6x + -3x2) = 0

Reorder the terms:
-16 + -2 + -6x + 4x2 + -3x2 = 0

Combine like terms: -16 + -2 = -18
-18 + -6x + 4x2 + -3x2 = 0

Combine like terms: 4x2 + -3x2 = 1x2
-18 + -6x + 1x2 = 0

Solving
-18 + -6x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -6x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -6x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -6x + x2 = 0 + 18
-6x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-6x + x2 = 18

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 18 + 9

Reorder the terms:
9 + -6x + x2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + -6x + x2 = 27

Factor a perfect square on the left side:
(x + -3)(x + -3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -3) equal to 5.196152423 and -5.196152423.


Subproblem 1
x + -3 = 5.196152423

Simplifying
x + -3 = 5.196152423

Reorder the terms:
-3 + x = 5.196152423

Solving
-3 + x = 5.196152423

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + x = 5.196152423 + 3
x = 5.196152423 + 3

Combine like terms: 5.196152423 + 3 = 8.196152423
x = 8.196152423

Simplifying
x = 8.196152423


Subproblem 2
x + -3 = -5.196152423

Simplifying
x + -3 = -5.196152423

Reorder the terms:
-3 + x = -5.196152423

Solving
-3 + x = -5.196152423

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + x = -5.196152423 + 3
x = -5.196152423 + 3

Combine like terms: -5.196152423 + 3 = -2.196152423
x = -2.196152423

Simplifying
x = -2.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.196152423, -2.196152423}

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