3x(5x+18)=90

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Solution for 3x(5x+18)=90 equation: 


Simplifying
3x(5x + 18) = 90

Reorder the terms:
3x(18 + 5x) = 90
(18 * 3x + 5x * 3x) = 90
(54x + 15x2) = 90

Solving
54x + 15x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 54x + 15x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 54x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 18x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-30 + 18x + 5x2)' equal to zero and attempt to solve:

Simplifying
-30 + 18x + 5x2 = 0

Solving
-30 + 18x + 5x2 = 0

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

Divide each side by '5'.
-6 + 3.6x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.6x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.6x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.6x + x2 = 0 + 6
3.6x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.6x + x2 = 6

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = 6 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = 6 + 3.24

Combine like terms: 6 + 3.24 = 9.24
3.24 + 3.6x + x2 = 9.24

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 9.24

Calculate the square root of the right side: 3.039736831

Break this problem into two subproblems by setting 
(x + 1.8) equal to 3.039736831 and -3.039736831.


Subproblem 1
x + 1.8 = 3.039736831

Simplifying
x + 1.8 = 3.039736831

Reorder the terms:
1.8 + x = 3.039736831

Solving
1.8 + x = 3.039736831

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = 3.039736831 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = 3.039736831 + -1.8
x = 3.039736831 + -1.8

Combine like terms: 3.039736831 + -1.8 = 1.239736831
x = 1.239736831

Simplifying
x = 1.239736831


Subproblem 2
x + 1.8 = -3.039736831

Simplifying
x + 1.8 = -3.039736831

Reorder the terms:
1.8 + x = -3.039736831

Solving
1.8 + x = -3.039736831

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = -3.039736831 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = -3.039736831 + -1.8
x = -3.039736831 + -1.8

Combine like terms: -3.039736831 + -1.8 = -4.839736831
x = -4.839736831

Simplifying
x = -4.839736831


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.239736831, -4.839736831}
Solution
x = {1.239736831, -4.839736831}

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