3x(x+16)=2(x-14)

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Solution for 3x(x+16)=2(x-14) equation: 


Simplifying
3x(x + 16) = 2(x + -14)

Reorder the terms:
3x(16 + x) = 2(x + -14)
(16 * 3x + x * 3x) = 2(x + -14)
(48x + 3x2) = 2(x + -14)

Reorder the terms:
48x + 3x2 = 2(-14 + x)
48x + 3x2 = (-14 * 2 + x * 2)
48x + 3x2 = (-28 + 2x)

Solving
48x + 3x2 = -28 + 2x

Solving for variable 'x'.

Reorder the terms:
28 + 48x + -2x + 3x2 = -28 + 2x + 28 + -2x

Combine like terms: 48x + -2x = 46x
28 + 46x + 3x2 = -28 + 2x + 28 + -2x

Reorder the terms:
28 + 46x + 3x2 = -28 + 28 + 2x + -2x

Combine like terms: -28 + 28 = 0
28 + 46x + 3x2 = 0 + 2x + -2x
28 + 46x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
28 + 46x + 3x2 = 0

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

Divide each side by '3'.
9.333333333 + 15.33333333x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + 15.33333333x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + 15.33333333x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + 15.33333333x + x2 = 0 + -9.333333333
15.33333333x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
15.33333333x + x2 = -9.333333333

The x term is 15.33333333x.  Take half its coefficient (7.666666665).
Square it (58.77777775) and add it to both sides.

Add '58.77777775' to each side of the equation.
15.33333333x + 58.77777775 + x2 = -9.333333333 + 58.77777775

Reorder the terms:
58.77777775 + 15.33333333x + x2 = -9.333333333 + 58.77777775

Combine like terms: -9.333333333 + 58.77777775 = 49.444444417
58.77777775 + 15.33333333x + x2 = 49.444444417

Factor a perfect square on the left side:
(x + 7.666666665)(x + 7.666666665) = 49.444444417

Calculate the square root of the right side: 7.031674368

Break this problem into two subproblems by setting 
(x + 7.666666665) equal to 7.031674368 and -7.031674368.


Subproblem 1
x + 7.666666665 = 7.031674368

Simplifying
x + 7.666666665 = 7.031674368

Reorder the terms:
7.666666665 + x = 7.031674368

Solving
7.666666665 + x = 7.031674368

Solving for variable 'x'.

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

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = 7.031674368 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = 7.031674368 + -7.666666665
x = 7.031674368 + -7.666666665

Combine like terms: 7.031674368 + -7.666666665 = -0.634992297
x = -0.634992297

Simplifying
x = -0.634992297


Subproblem 2
x + 7.666666665 = -7.031674368

Simplifying
x + 7.666666665 = -7.031674368

Reorder the terms:
7.666666665 + x = -7.031674368

Solving
7.666666665 + x = -7.031674368

Solving for variable 'x'.

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

Add '-7.666666665' to each side of the equation.
7.666666665 + -7.666666665 + x = -7.031674368 + -7.666666665

Combine like terms: 7.666666665 + -7.666666665 = 0.000000000
0.000000000 + x = -7.031674368 + -7.666666665
x = -7.031674368 + -7.666666665

Combine like terms: -7.031674368 + -7.666666665 = -14.698341033
x = -14.698341033

Simplifying
x = -14.698341033


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.634992297, -14.698341033}

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