18x+40x(x-3)=468

Solution for 18x+40x(x-3)=468 equation:

Simplifying
18x + 40x(x + -3) = 468

Reorder the terms:
18x + 40x(-3 + x) = 468
18x + (-3 * 40x + x * 40x) = 468
18x + (-120x + 40x2) = 468

Combine like terms: 18x + -120x = -102x
-102x + 40x2 = 468

Solving
-102x + 40x2 = 468

Solving for variable 'x'.

Reorder the terms:
-468 + -102x + 40x2 = 468 + -468

Combine like terms: 468 + -468 = 0
-468 + -102x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-234 + -51x + 20x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-234 + -51x + 20x2)' equal to zero and attempt to solve:

Simplifying
-234 + -51x + 20x2 = 0

Solving
-234 + -51x + 20x2 = 0

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

Divide each side by '20'.
-11.7 + -2.55x + x2 = 0.0

Move the constant term to the right:

Add '11.7' to each side of the equation.
-11.7 + -2.55x + 11.7 + x2 = 0.0 + 11.7

Reorder the terms:
-11.7 + 11.7 + -2.55x + x2 = 0.0 + 11.7

Combine like terms: -11.7 + 11.7 = 0.0
0.0 + -2.55x + x2 = 0.0 + 11.7
-2.55x + x2 = 0.0 + 11.7

Combine like terms: 0.0 + 11.7 = 11.7
-2.55x + x2 = 11.7

The x term is -2.55x.  Take half its coefficient (-1.275).
Square it (1.625625) and add it to both sides.

Add '1.625625' to each side of the equation.
-2.55x + 1.625625 + x2 = 11.7 + 1.625625

Reorder the terms:
1.625625 + -2.55x + x2 = 11.7 + 1.625625

Combine like terms: 11.7 + 1.625625 = 13.325625
1.625625 + -2.55x + x2 = 13.325625

Factor a perfect square on the left side:
(x + -1.275)(x + -1.275) = 13.325625

Calculate the square root of the right side: 3.650428057

Break this problem into two subproblems by setting 
(x + -1.275) equal to 3.650428057 and -3.650428057.

Subproblem 1
x + -1.275 = 3.650428057

Simplifying
x + -1.275 = 3.650428057

Reorder the terms:
-1.275 + x = 3.650428057

Solving
-1.275 + x = 3.650428057

Solving for variable 'x'.

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

Add '1.275' to each side of the equation.
-1.275 + 1.275 + x = 3.650428057 + 1.275

Combine like terms: -1.275 + 1.275 = 0.000
0.000 + x = 3.650428057 + 1.275
x = 3.650428057 + 1.275

Combine like terms: 3.650428057 + 1.275 = 4.925428057
x = 4.925428057

Simplifying
x = 4.925428057

Subproblem 2
x + -1.275 = -3.650428057

Simplifying
x + -1.275 = -3.650428057

Reorder the terms:
-1.275 + x = -3.650428057

Solving
-1.275 + x = -3.650428057

Solving for variable 'x'.

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

Add '1.275' to each side of the equation.
-1.275 + 1.275 + x = -3.650428057 + 1.275

Combine like terms: -1.275 + 1.275 = 0.000
0.000 + x = -3.650428057 + 1.275
x = -3.650428057 + 1.275

Combine like terms: -3.650428057 + 1.275 = -2.375428057
x = -2.375428057

Simplifying
x = -2.375428057

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.925428057, -2.375428057}
Solution
x = {4.925428057, -2.375428057}