5x(3x-18)=30-4(6x-9)

Solution for 5x(3x-18)=30-4(6x-9) equation:

Simplifying
5x(3x + -18) = 30 + -4(6x + -9)

Reorder the terms:
5x(-18 + 3x) = 30 + -4(6x + -9)
(-18 * 5x + 3x * 5x) = 30 + -4(6x + -9)
(-90x + 15x2) = 30 + -4(6x + -9)

Reorder the terms:
-90x + 15x2 = 30 + -4(-9 + 6x)
-90x + 15x2 = 30 + (-9 * -4 + 6x * -4)
-90x + 15x2 = 30 + (36 + -24x)

Combine like terms: 30 + 36 = 66
-90x + 15x2 = 66 + -24x

Solving
-90x + 15x2 = 66 + -24x

Solving for variable 'x'.

Reorder the terms:
-66 + -90x + 24x + 15x2 = 66 + -24x + -66 + 24x

Combine like terms: -90x + 24x = -66x
-66 + -66x + 15x2 = 66 + -24x + -66 + 24x

Reorder the terms:
-66 + -66x + 15x2 = 66 + -66 + -24x + 24x

Combine like terms: 66 + -66 = 0
-66 + -66x + 15x2 = 0 + -24x + 24x
-66 + -66x + 15x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-66 + -66x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + -22x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-22 + -22x + 5x2)' equal to zero and attempt to solve:

Simplifying
-22 + -22x + 5x2 = 0

Solving
-22 + -22x + 5x2 = 0

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

Divide each side by '5'.
-4.4 + -4.4x + x2 = 0

Move the constant term to the right:

Add '4.4' to each side of the equation.
-4.4 + -4.4x + 4.4 + x2 = 0 + 4.4

Reorder the terms:
-4.4 + 4.4 + -4.4x + x2 = 0 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + -4.4x + x2 = 0 + 4.4
-4.4x + x2 = 0 + 4.4

Combine like terms: 0 + 4.4 = 4.4
-4.4x + x2 = 4.4

The x term is -4.4x.  Take half its coefficient (-2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
-4.4x + 4.84 + x2 = 4.4 + 4.84

Reorder the terms:
4.84 + -4.4x + x2 = 4.4 + 4.84

Combine like terms: 4.4 + 4.84 = 9.24
4.84 + -4.4x + x2 = 9.24

Factor a perfect square on the left side:
(x + -2.2)(x + -2.2) = 9.24

Calculate the square root of the right side: 3.039736831

Break this problem into two subproblems by setting 
(x + -2.2) equal to 3.039736831 and -3.039736831.

Subproblem 1
x + -2.2 = 3.039736831

Simplifying
x + -2.2 = 3.039736831

Reorder the terms:
-2.2 + x = 3.039736831

Solving
-2.2 + x = 3.039736831

Solving for variable 'x'.

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

Add '2.2' to each side of the equation.
-2.2 + 2.2 + x = 3.039736831 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + x = 3.039736831 + 2.2
x = 3.039736831 + 2.2

Combine like terms: 3.039736831 + 2.2 = 5.239736831
x = 5.239736831

Simplifying
x = 5.239736831

Subproblem 2
x + -2.2 = -3.039736831

Simplifying
x + -2.2 = -3.039736831

Reorder the terms:
-2.2 + x = -3.039736831

Solving
-2.2 + x = -3.039736831

Solving for variable 'x'.

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

Add '2.2' to each side of the equation.
-2.2 + 2.2 + x = -3.039736831 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + x = -3.039736831 + 2.2
x = -3.039736831 + 2.2

Combine like terms: -3.039736831 + 2.2 = -0.839736831
x = -0.839736831

Simplifying
x = -0.839736831

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.239736831, -0.839736831}
Solution
x = {5.239736831, -0.839736831}