3x(x+4)+2=12

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Solution for 3x(x+4)+2=12 equation:


Simplifying
3x(x + 4) + 2 = 12

Reorder the terms:
3x(4 + x) + 2 = 12
(4 * 3x + x * 3x) + 2 = 12
(12x + 3x2) + 2 = 12

Reorder the terms:
2 + 12x + 3x2 = 12

Solving
2 + 12x + 3x2 = 12

Solving for variable 'x'.

Reorder the terms:
2 + -12 + 12x + 3x2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + 12x + 3x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + 12x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + 4x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 4x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 4x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + 3.333333333
4x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
4x + x2 = 3.333333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 3.333333333 + 4

Reorder the terms:
4 + 4x + x2 = 3.333333333 + 4

Combine like terms: 3.333333333 + 4 = 7.333333333
4 + 4x + x2 = 7.333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 7.333333333

Calculate the square root of the right side: 2.708012801

Break this problem into two subproblems by setting 
(x + 2) equal to 2.708012801 and -2.708012801.


Subproblem 1
x + 2 = 2.708012801

Simplifying
x + 2 = 2.708012801

Reorder the terms:
2 + x = 2.708012801

Solving
2 + x = 2.708012801

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.708012801 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.708012801 + -2
x = 2.708012801 + -2

Combine like terms: 2.708012801 + -2 = 0.708012801
x = 0.708012801

Simplifying
x = 0.708012801


Subproblem 2
x + 2 = -2.708012801

Simplifying
x + 2 = -2.708012801

Reorder the terms:
2 + x = -2.708012801

Solving
2 + x = -2.708012801

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.708012801 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.708012801 + -2
x = -2.708012801 + -2

Combine like terms: -2.708012801 + -2 = -4.708012801
x = -4.708012801

Simplifying
x = -4.708012801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.708012801, -4.708012801}

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