3x(x+40)=180

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


Simplifying
3x(x + 40) = 180

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

Solving
120x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 120x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 120x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 40x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 40x + x2)' equal to zero and attempt to solve:

Simplifying
-60 + 40x + x2 = 0

Solving
-60 + 40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 40x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 40x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 40x + x2 = 0 + 60
40x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
40x + x2 = 60

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = 60 + 400

Reorder the terms:
400 + 40x + x2 = 60 + 400

Combine like terms: 60 + 400 = 460
400 + 40x + x2 = 460

Factor a perfect square on the left side:
(x + 20)(x + 20) = 460

Calculate the square root of the right side: 21.44761059

Break this problem into two subproblems by setting 
(x + 20) equal to 21.44761059 and -21.44761059.


Subproblem 1
x + 20 = 21.44761059

Simplifying
x + 20 = 21.44761059

Reorder the terms:
20 + x = 21.44761059

Solving
20 + x = 21.44761059

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 21.44761059 + -20

Combine like terms: 20 + -20 = 0
0 + x = 21.44761059 + -20
x = 21.44761059 + -20

Combine like terms: 21.44761059 + -20 = 1.44761059
x = 1.44761059

Simplifying
x = 1.44761059


Subproblem 2
x + 20 = -21.44761059

Simplifying
x + 20 = -21.44761059

Reorder the terms:
20 + x = -21.44761059

Solving
20 + x = -21.44761059

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -21.44761059 + -20

Combine like terms: 20 + -20 = 0
0 + x = -21.44761059 + -20
x = -21.44761059 + -20

Combine like terms: -21.44761059 + -20 = -41.44761059
x = -41.44761059

Simplifying
x = -41.44761059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.44761059, -41.44761059}
Solution
x = {1.44761059, -41.44761059}

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