3(x+5)(x+5)=60

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Solution for 3(x+5)(x+5)=60 equation: 


Simplifying
3(x + 5)(x + 5) = 60

Reorder the terms:
3(5 + x)(x + 5) = 60

Reorder the terms:
3(5 + x)(5 + x) = 60

Multiply (5 + x) * (5 + x)
3(5(5 + x) + x(5 + x)) = 60
3((5 * 5 + x * 5) + x(5 + x)) = 60
3((25 + 5x) + x(5 + x)) = 60
3(25 + 5x + (5 * x + x * x)) = 60
3(25 + 5x + (5x + x2)) = 60

Combine like terms: 5x + 5x = 10x
3(25 + 10x + x2) = 60
(25 * 3 + 10x * 3 + x2 * 3) = 60
(75 + 30x + 3x2) = 60

Solving
75 + 30x + 3x2 = 60

Solving for variable 'x'.

Reorder the terms:
75 + -60 + 30x + 3x2 = 60 + -60

Combine like terms: 75 + -60 = 15
15 + 30x + 3x2 = 60 + -60

Combine like terms: 60 + -60 = 0
15 + 30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 10x + x2 = 0

Solving
5 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 10x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 10x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 10x + x2 = 0 + -5
10x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
10x + x2 = -5

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 = -5 + 25

Reorder the terms:
25 + 10x + x2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + 10x + x2 = 20

Factor a perfect square on the left side:
(x + 5)(x + 5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + 5) equal to 4.472135955 and -4.472135955.


Subproblem 1
x + 5 = 4.472135955

Simplifying
x + 5 = 4.472135955

Reorder the terms:
5 + x = 4.472135955

Solving
5 + x = 4.472135955

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 = 4.472135955 + -5

Combine like terms: 5 + -5 = 0
0 + x = 4.472135955 + -5
x = 4.472135955 + -5

Combine like terms: 4.472135955 + -5 = -0.527864045
x = -0.527864045

Simplifying
x = -0.527864045


Subproblem 2
x + 5 = -4.472135955

Simplifying
x + 5 = -4.472135955

Reorder the terms:
5 + x = -4.472135955

Solving
5 + x = -4.472135955

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 = -4.472135955 + -5

Combine like terms: 5 + -5 = 0
0 + x = -4.472135955 + -5
x = -4.472135955 + -5

Combine like terms: -4.472135955 + -5 = -9.472135955
x = -9.472135955

Simplifying
x = -9.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.527864045, -9.472135955}
Solution
x = {-0.527864045, -9.472135955}

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