(5x+15)(5x+15)=45

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Solution for (5x+15)(5x+15)=45 equation: 


Simplifying
(5x + 15)(5x + 15) = 45

Reorder the terms:
(15 + 5x)(5x + 15) = 45

Reorder the terms:
(15 + 5x)(15 + 5x) = 45

Multiply (15 + 5x) * (15 + 5x)
(15(15 + 5x) + 5x * (15 + 5x)) = 45
((15 * 15 + 5x * 15) + 5x * (15 + 5x)) = 45
((225 + 75x) + 5x * (15 + 5x)) = 45
(225 + 75x + (15 * 5x + 5x * 5x)) = 45
(225 + 75x + (75x + 25x2)) = 45

Combine like terms: 75x + 75x = 150x
(225 + 150x + 25x2) = 45

Solving
225 + 150x + 25x2 = 45

Solving for variable 'x'.

Reorder the terms:
225 + -45 + 150x + 25x2 = 45 + -45

Combine like terms: 225 + -45 = 180
180 + 150x + 25x2 = 45 + -45

Combine like terms: 45 + -45 = 0
180 + 150x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(36 + 30x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(36 + 30x + 5x2)' equal to zero and attempt to solve:

Simplifying
36 + 30x + 5x2 = 0

Solving
36 + 30x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
7.2 + 6x + x2 = 0

Move the constant term to the right:

Add '-7.2' to each side of the equation.
7.2 + 6x + -7.2 + x2 = 0 + -7.2

Reorder the terms:
7.2 + -7.2 + 6x + x2 = 0 + -7.2

Combine like terms: 7.2 + -7.2 = 0.0
0.0 + 6x + x2 = 0 + -7.2
6x + x2 = 0 + -7.2

Combine like terms: 0 + -7.2 = -7.2
6x + x2 = -7.2

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -7.2 + 9

Reorder the terms:
9 + 6x + x2 = -7.2 + 9

Combine like terms: -7.2 + 9 = 1.8
9 + 6x + x2 = 1.8

Factor a perfect square on the left side:
(x + 3)(x + 3) = 1.8

Calculate the square root of the right side: 1.341640787

Break this problem into two subproblems by setting 
(x + 3) equal to 1.341640787 and -1.341640787.


Subproblem 1
x + 3 = 1.341640787

Simplifying
x + 3 = 1.341640787

Reorder the terms:
3 + x = 1.341640787

Solving
3 + x = 1.341640787

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1.341640787 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.341640787 + -3
x = 1.341640787 + -3

Combine like terms: 1.341640787 + -3 = -1.658359213
x = -1.658359213

Simplifying
x = -1.658359213


Subproblem 2
x + 3 = -1.341640787

Simplifying
x + 3 = -1.341640787

Reorder the terms:
3 + x = -1.341640787

Solving
3 + x = -1.341640787

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1.341640787 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.341640787 + -3
x = -1.341640787 + -3

Combine like terms: -1.341640787 + -3 = -4.341640787
x = -4.341640787

Simplifying
x = -4.341640787


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.658359213, -4.341640787}
Solution
x = {-1.658359213, -4.341640787}

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