4x(3x-9)=162

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Solution for 4x(3x-9)=162 equation: 


Simplifying
4x(3x + -9) = 162

Reorder the terms:
4x(-9 + 3x) = 162
(-9 * 4x + 3x * 4x) = 162
(-36x + 12x2) = 162

Solving
-36x + 12x2 = 162

Solving for variable 'x'.

Reorder the terms:
-162 + -36x + 12x2 = 162 + -162

Combine like terms: 162 + -162 = 0
-162 + -36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-27 + -6x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-27 + -6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-27 + -6x + 2x2 = 0

Solving
-27 + -6x + 2x2 = 0

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

Divide each side by '2'.
-13.5 + -3x + x2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -3x + 13.5 + x2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -3x + x2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -3x + x2 = 0 + 13.5
-3x + x2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-3x + x2 = 13.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 13.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 13.5 + 2.25

Combine like terms: 13.5 + 2.25 = 15.75
2.25 + -3x + x2 = 15.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.968626967 and -3.968626967.


Subproblem 1
x + -1.5 = 3.968626967

Simplifying
x + -1.5 = 3.968626967

Reorder the terms:
-1.5 + x = 3.968626967

Solving
-1.5 + x = 3.968626967

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.968626967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.968626967 + 1.5
x = 3.968626967 + 1.5

Combine like terms: 3.968626967 + 1.5 = 5.468626967
x = 5.468626967

Simplifying
x = 5.468626967


Subproblem 2
x + -1.5 = -3.968626967

Simplifying
x + -1.5 = -3.968626967

Reorder the terms:
-1.5 + x = -3.968626967

Solving
-1.5 + x = -3.968626967

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.968626967 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.968626967 + 1.5
x = -3.968626967 + 1.5

Combine like terms: -3.968626967 + 1.5 = -2.468626967
x = -2.468626967

Simplifying
x = -2.468626967


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.468626967, -2.468626967}
Solution
x = {5.468626967, -2.468626967}

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