(3X+30)(4X)=360

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Solution for (3X+30)(4X)=360 equation: 


Simplifying
(3X + 30)(4X) = 360

Reorder the terms:
(30 + 3X)(4X) = 360

Remove parenthesis around (4X)
(30 + 3X) * 4X = 360

Reorder the terms for easier multiplication:
4X(30 + 3X) = 360
(30 * 4X + 3X * 4X) = 360
(120X + 12X2) = 360

Solving
120X + 12X2 = 360

Solving for variable 'X'.

Reorder the terms:
-360 + 120X + 12X2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 120X + 12X2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-30 + 10X + X2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-30 + 10X + X2)' equal to zero and attempt to solve:

Simplifying
-30 + 10X + X2 = 0

Solving
-30 + 10X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 10X + 30 + X2 = 0 + 30

Reorder the terms:
-30 + 30 + 10X + X2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 10X + X2 = 0 + 30
10X + X2 = 0 + 30

Combine like terms: 0 + 30 = 30
10X + X2 = 30

The X term is 10X.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10X + 25 + X2 = 30 + 25

Reorder the terms:
25 + 10X + X2 = 30 + 25

Combine like terms: 30 + 25 = 55
25 + 10X + X2 = 55

Factor a perfect square on the left side:
(X + 5)(X + 5) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(X + 5) equal to 7.416198487 and -7.416198487.


Subproblem 1
X + 5 = 7.416198487

Simplifying
X + 5 = 7.416198487

Reorder the terms:
5 + X = 7.416198487

Solving
5 + X = 7.416198487

Solving for variable 'X'.

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

Add '-5' to each side of the equation.
5 + -5 + X = 7.416198487 + -5

Combine like terms: 5 + -5 = 0
0 + X = 7.416198487 + -5
X = 7.416198487 + -5

Combine like terms: 7.416198487 + -5 = 2.416198487
X = 2.416198487

Simplifying
X = 2.416198487


Subproblem 2
X + 5 = -7.416198487

Simplifying
X + 5 = -7.416198487

Reorder the terms:
5 + X = -7.416198487

Solving
5 + X = -7.416198487

Solving for variable 'X'.

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

Add '-5' to each side of the equation.
5 + -5 + X = -7.416198487 + -5

Combine like terms: 5 + -5 = 0
0 + X = -7.416198487 + -5
X = -7.416198487 + -5

Combine like terms: -7.416198487 + -5 = -12.416198487
X = -12.416198487

Simplifying
X = -12.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.416198487, -12.416198487}
Solution
X = {2.416198487, -12.416198487}

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