3x(2x+20)=120

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Solution for 3x(2x+20)=120 equation: 


Simplifying
3x(2x + 20) = 120

Reorder the terms:
3x(20 + 2x) = 120
(20 * 3x + 2x * 3x) = 120
(60x + 6x2) = 120

Solving
60x + 6x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 60x + 6x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 60x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-20 + 10x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-20 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + 10x + x2 = 0

Solving
-20 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 10x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 10x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 10x + x2 = 0 + 20
10x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
10x + x2 = 20

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 = 20 + 25

Reorder the terms:
25 + 10x + x2 = 20 + 25

Combine like terms: 20 + 25 = 45
25 + 10x + x2 = 45

Factor a perfect square on the left side:
(x + 5)(x + 5) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 5) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + 5 = 6.708203933

Simplifying
x + 5 = 6.708203933

Reorder the terms:
5 + x = 6.708203933

Solving
5 + x = 6.708203933

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 = 6.708203933 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.708203933 + -5
x = 6.708203933 + -5

Combine like terms: 6.708203933 + -5 = 1.708203933
x = 1.708203933

Simplifying
x = 1.708203933


Subproblem 2
x + 5 = -6.708203933

Simplifying
x + 5 = -6.708203933

Reorder the terms:
5 + x = -6.708203933

Solving
5 + x = -6.708203933

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 = -6.708203933 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.708203933 + -5
x = -6.708203933 + -5

Combine like terms: -6.708203933 + -5 = -11.708203933
x = -11.708203933

Simplifying
x = -11.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.708203933, -11.708203933}
Solution
x = {1.708203933, -11.708203933}

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