360=3x(80-x)

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Solution for 360=3x(80-x) equation: 


Simplifying
360 = 3x(80 + -1x)
360 = (80 * 3x + -1x * 3x)
360 = (240x + -3x2)

Solving
360 = 240x + -3x2

Solving for variable 'x'.

Reorder the terms:
360 + -240x + 3x2 = 240x + -240x + -3x2 + 3x2

Combine like terms: 240x + -240x = 0
360 + -240x + 3x2 = 0 + -3x2 + 3x2
360 + -240x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
360 + -240x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(120 + -80x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(120 + -80x + x2)' equal to zero and attempt to solve:

Simplifying
120 + -80x + x2 = 0

Solving
120 + -80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -80x + -120 + x2 = 0 + -120

Reorder the terms:
120 + -120 + -80x + x2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -80x + x2 = 0 + -120
-80x + x2 = 0 + -120

Combine like terms: 0 + -120 = -120
-80x + x2 = -120

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = -120 + 1600

Reorder the terms:
1600 + -80x + x2 = -120 + 1600

Combine like terms: -120 + 1600 = 1480
1600 + -80x + x2 = 1480

Factor a perfect square on the left side:
(x + -40)(x + -40) = 1480

Calculate the square root of the right side: 38.470768123

Break this problem into two subproblems by setting 
(x + -40) equal to 38.470768123 and -38.470768123.


Subproblem 1
x + -40 = 38.470768123

Simplifying
x + -40 = 38.470768123

Reorder the terms:
-40 + x = 38.470768123

Solving
-40 + x = 38.470768123

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = 38.470768123 + 40

Combine like terms: -40 + 40 = 0
0 + x = 38.470768123 + 40
x = 38.470768123 + 40

Combine like terms: 38.470768123 + 40 = 78.470768123
x = 78.470768123

Simplifying
x = 78.470768123


Subproblem 2
x + -40 = -38.470768123

Simplifying
x + -40 = -38.470768123

Reorder the terms:
-40 + x = -38.470768123

Solving
-40 + x = -38.470768123

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = -38.470768123 + 40

Combine like terms: -40 + 40 = 0
0 + x = -38.470768123 + 40
x = -38.470768123 + 40

Combine like terms: -38.470768123 + 40 = 1.529231877
x = 1.529231877

Simplifying
x = 1.529231877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {78.470768123, 1.529231877}
Solution
x = {78.470768123, 1.529231877}

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