3x(2x+40)=180

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Solution for 3x(2x+40)=180 equation: 


Simplifying
3x(2x + 40) = 180

Reorder the terms:
3x(40 + 2x) = 180
(40 * 3x + 2x * 3x) = 180
(120x + 6x2) = 180

Solving
120x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 120x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 120x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 20x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-30 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 20x + x2 = 0

Solving
-30 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 20x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 20x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 20x + x2 = 0 + 30
20x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
20x + x2 = 30

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 30 + 100

Reorder the terms:
100 + 20x + x2 = 30 + 100

Combine like terms: 30 + 100 = 130
100 + 20x + x2 = 130

Factor a perfect square on the left side:
(x + 10)(x + 10) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(x + 10) equal to 11.401754251 and -11.401754251.


Subproblem 1
x + 10 = 11.401754251

Simplifying
x + 10 = 11.401754251

Reorder the terms:
10 + x = 11.401754251

Solving
10 + x = 11.401754251

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 11.401754251 + -10

Combine like terms: 10 + -10 = 0
0 + x = 11.401754251 + -10
x = 11.401754251 + -10

Combine like terms: 11.401754251 + -10 = 1.401754251
x = 1.401754251

Simplifying
x = 1.401754251


Subproblem 2
x + 10 = -11.401754251

Simplifying
x + 10 = -11.401754251

Reorder the terms:
10 + x = -11.401754251

Solving
10 + x = -11.401754251

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -11.401754251 + -10

Combine like terms: 10 + -10 = 0
0 + x = -11.401754251 + -10
x = -11.401754251 + -10

Combine like terms: -11.401754251 + -10 = -21.401754251
x = -21.401754251

Simplifying
x = -21.401754251


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.401754251, -21.401754251}
Solution
x = {1.401754251, -21.401754251}

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