3x(x-7)=138+3x

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Solution for 3x(x-7)=138+3x equation: 


Simplifying
3x(x + -7) = 138 + 3x

Reorder the terms:
3x(-7 + x) = 138 + 3x
(-7 * 3x + x * 3x) = 138 + 3x
(-21x + 3x2) = 138 + 3x

Solving
-21x + 3x2 = 138 + 3x

Solving for variable 'x'.

Reorder the terms:
-138 + -21x + -3x + 3x2 = 138 + 3x + -138 + -3x

Combine like terms: -21x + -3x = -24x
-138 + -24x + 3x2 = 138 + 3x + -138 + -3x

Reorder the terms:
-138 + -24x + 3x2 = 138 + -138 + 3x + -3x

Combine like terms: 138 + -138 = 0
-138 + -24x + 3x2 = 0 + 3x + -3x
-138 + -24x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-138 + -24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-46 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-46 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-46 + -8x + x2 = 0

Solving
-46 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + -8x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + -8x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -8x + x2 = 0 + 46
-8x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
-8x + x2 = 46

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 = 46 + 16

Reorder the terms:
16 + -8x + x2 = 46 + 16

Combine like terms: 46 + 16 = 62
16 + -8x + x2 = 62

Factor a perfect square on the left side:
(x + -4)(x + -4) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(x + -4) equal to 7.874007874 and -7.874007874.


Subproblem 1
x + -4 = 7.874007874

Simplifying
x + -4 = 7.874007874

Reorder the terms:
-4 + x = 7.874007874

Solving
-4 + x = 7.874007874

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 = 7.874007874 + 4

Combine like terms: -4 + 4 = 0
0 + x = 7.874007874 + 4
x = 7.874007874 + 4

Combine like terms: 7.874007874 + 4 = 11.874007874
x = 11.874007874

Simplifying
x = 11.874007874


Subproblem 2
x + -4 = -7.874007874

Simplifying
x + -4 = -7.874007874

Reorder the terms:
-4 + x = -7.874007874

Solving
-4 + x = -7.874007874

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 = -7.874007874 + 4

Combine like terms: -4 + 4 = 0
0 + x = -7.874007874 + 4
x = -7.874007874 + 4

Combine like terms: -7.874007874 + 4 = -3.874007874
x = -3.874007874

Simplifying
x = -3.874007874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.874007874, -3.874007874}
Solution
x = {11.874007874, -3.874007874}

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