3x(x+76)=180

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Solution for 3x(x+76)=180 equation: 


Simplifying
3x(x + 76) = 180

Reorder the terms:
3x(76 + x) = 180
(76 * 3x + x * 3x) = 180
(228x + 3x2) = 180

Solving
228x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 228x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 228x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 76x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 76x + x2)' equal to zero and attempt to solve:

Simplifying
-60 + 76x + x2 = 0

Solving
-60 + 76x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 76x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 76x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 76x + x2 = 0 + 60
76x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
76x + x2 = 60

The x term is 76x.  Take half its coefficient (38).
Square it (1444) and add it to both sides.

Add '1444' to each side of the equation.
76x + 1444 + x2 = 60 + 1444

Reorder the terms:
1444 + 76x + x2 = 60 + 1444

Combine like terms: 60 + 1444 = 1504
1444 + 76x + x2 = 1504

Factor a perfect square on the left side:
(x + 38)(x + 38) = 1504

Calculate the square root of the right side: 38.781438859

Break this problem into two subproblems by setting 
(x + 38) equal to 38.781438859 and -38.781438859.


Subproblem 1
x + 38 = 38.781438859

Simplifying
x + 38 = 38.781438859

Reorder the terms:
38 + x = 38.781438859

Solving
38 + x = 38.781438859

Solving for variable 'x'.

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

Add '-38' to each side of the equation.
38 + -38 + x = 38.781438859 + -38

Combine like terms: 38 + -38 = 0
0 + x = 38.781438859 + -38
x = 38.781438859 + -38

Combine like terms: 38.781438859 + -38 = 0.781438859
x = 0.781438859

Simplifying
x = 0.781438859


Subproblem 2
x + 38 = -38.781438859

Simplifying
x + 38 = -38.781438859

Reorder the terms:
38 + x = -38.781438859

Solving
38 + x = -38.781438859

Solving for variable 'x'.

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

Add '-38' to each side of the equation.
38 + -38 + x = -38.781438859 + -38

Combine like terms: 38 + -38 = 0
0 + x = -38.781438859 + -38
x = -38.781438859 + -38

Combine like terms: -38.781438859 + -38 = -76.781438859
x = -76.781438859

Simplifying
x = -76.781438859


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.781438859, -76.781438859}
Solution
x = {0.781438859, -76.781438859}

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