(x^2+18x+30)=4(x^2+18x+45)

Solution for (x^2+18x+30)=4(x^2+18x+45) equation:

Simplifying
(x2 + 18x + 30) = 4(x2 + 18x + 45)

Reorder the terms:
(30 + 18x + x2) = 4(x2 + 18x + 45)

Remove parenthesis around (30 + 18x + x2)
30 + 18x + x2 = 4(x2 + 18x + 45)

Reorder the terms:
30 + 18x + x2 = 4(45 + 18x + x2)
30 + 18x + x2 = (45 * 4 + 18x * 4 + x2 * 4)
30 + 18x + x2 = (180 + 72x + 4x2)

Solving
30 + 18x + x2 = 180 + 72x + 4x2

Solving for variable 'x'.

Reorder the terms:
30 + -180 + 18x + -72x + x2 + -4x2 = 180 + 72x + 4x2 + -180 + -72x + -4x2

Combine like terms: 30 + -180 = -150
-150 + 18x + -72x + x2 + -4x2 = 180 + 72x + 4x2 + -180 + -72x + -4x2

Combine like terms: 18x + -72x = -54x
-150 + -54x + x2 + -4x2 = 180 + 72x + 4x2 + -180 + -72x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-150 + -54x + -3x2 = 180 + 72x + 4x2 + -180 + -72x + -4x2

Reorder the terms:
-150 + -54x + -3x2 = 180 + -180 + 72x + -72x + 4x2 + -4x2

Combine like terms: 180 + -180 = 0
-150 + -54x + -3x2 = 0 + 72x + -72x + 4x2 + -4x2
-150 + -54x + -3x2 = 72x + -72x + 4x2 + -4x2

Combine like terms: 72x + -72x = 0
-150 + -54x + -3x2 = 0 + 4x2 + -4x2
-150 + -54x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-150 + -54x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(50 + 18x + x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(50 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
50 + 18x + x2 = 0

Solving
50 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + 18x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + 18x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 18x + x2 = 0 + -50
18x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
18x + x2 = -50

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -50 + 81

Reorder the terms:
81 + 18x + x2 = -50 + 81

Combine like terms: -50 + 81 = 31
81 + 18x + x2 = 31

Factor a perfect square on the left side:
(x + 9)(x + 9) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 9) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + 9 = 5.567764363

Simplifying
x + 9 = 5.567764363

Reorder the terms:
9 + x = 5.567764363

Solving
9 + x = 5.567764363

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 5.567764363 + -9

Combine like terms: 9 + -9 = 0
0 + x = 5.567764363 + -9
x = 5.567764363 + -9

Combine like terms: 5.567764363 + -9 = -3.432235637
x = -3.432235637

Simplifying
x = -3.432235637

Subproblem 2
x + 9 = -5.567764363

Simplifying
x + 9 = -5.567764363

Reorder the terms:
9 + x = -5.567764363

Solving
9 + x = -5.567764363

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -5.567764363 + -9

Combine like terms: 9 + -9 = 0
0 + x = -5.567764363 + -9
x = -5.567764363 + -9

Combine like terms: -5.567764363 + -9 = -14.567764363
x = -14.567764363

Simplifying
x = -14.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.432235637, -14.567764363}
Solution
x = {-3.432235637, -14.567764363}