3x+2x(x+12)+(2x+4)=360

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Solution for 3x+2x(x+12)+(2x+4)=360 equation:


Simplifying
3x + 2x(x + 12) + (2x + 4) = 360

Reorder the terms:
3x + 2x(12 + x) + (2x + 4) = 360
3x + (12 * 2x + x * 2x) + (2x + 4) = 360
3x + (24x + 2x2) + (2x + 4) = 360

Reorder the terms:
3x + 24x + 2x2 + (4 + 2x) = 360

Remove parenthesis around (4 + 2x)
3x + 24x + 2x2 + 4 + 2x = 360

Reorder the terms:
4 + 3x + 24x + 2x + 2x2 = 360

Combine like terms: 3x + 24x = 27x
4 + 27x + 2x + 2x2 = 360

Combine like terms: 27x + 2x = 29x
4 + 29x + 2x2 = 360

Solving
4 + 29x + 2x2 = 360

Solving for variable 'x'.

Reorder the terms:
4 + -360 + 29x + 2x2 = 360 + -360

Combine like terms: 4 + -360 = -356
-356 + 29x + 2x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-356 + 29x + 2x2 = 0

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

Divide each side by '2'.
-178 + 14.5x + x2 = 0

Move the constant term to the right:

Add '178' to each side of the equation.
-178 + 14.5x + 178 + x2 = 0 + 178

Reorder the terms:
-178 + 178 + 14.5x + x2 = 0 + 178

Combine like terms: -178 + 178 = 0
0 + 14.5x + x2 = 0 + 178
14.5x + x2 = 0 + 178

Combine like terms: 0 + 178 = 178
14.5x + x2 = 178

The x term is 14.5x.  Take half its coefficient (7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
14.5x + 52.5625 + x2 = 178 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = 178 + 52.5625

Combine like terms: 178 + 52.5625 = 230.5625
52.5625 + 14.5x + x2 = 230.5625

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 230.5625

Calculate the square root of the right side: 15.184284639

Break this problem into two subproblems by setting 
(x + 7.25) equal to 15.184284639 and -15.184284639.

Subproblem 1

x + 7.25 = 15.184284639 Simplifying x + 7.25 = 15.184284639 Reorder the terms: 7.25 + x = 15.184284639 Solving 7.25 + x = 15.184284639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 15.184284639 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 15.184284639 + -7.25 x = 15.184284639 + -7.25 Combine like terms: 15.184284639 + -7.25 = 7.934284639 x = 7.934284639 Simplifying x = 7.934284639

Subproblem 2

x + 7.25 = -15.184284639 Simplifying x + 7.25 = -15.184284639 Reorder the terms: 7.25 + x = -15.184284639 Solving 7.25 + x = -15.184284639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -15.184284639 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -15.184284639 + -7.25 x = -15.184284639 + -7.25 Combine like terms: -15.184284639 + -7.25 = -22.434284639 x = -22.434284639 Simplifying x = -22.434284639

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.934284639, -22.434284639}

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