3(4x^2-9x-6)=0

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Solution for 3(4x^2-9x-6)=0 equation: 


Simplifying
3(4x2 + -9x + -6) = 0

Reorder the terms:
3(-6 + -9x + 4x2) = 0
(-6 * 3 + -9x * 3 + 4x2 * 3) = 0
(-18 + -27x + 12x2) = 0

Solving
-18 + -27x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -9x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-6 + -9x + 4x2)' equal to zero and attempt to solve:

Simplifying
-6 + -9x + 4x2 = 0

Solving
-6 + -9x + 4x2 = 0

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

Divide each side by '4'.
-1.5 + -2.25x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2.25x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2.25x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2.25x + x2 = 0 + 1.5
-2.25x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2.25x + x2 = 1.5

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 1.5 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 1.5 + 1.265625

Combine like terms: 1.5 + 1.265625 = 2.765625
1.265625 + -2.25x + x2 = 2.765625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 2.765625

Calculate the square root of the right side: 1.663016837

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.663016837 and -1.663016837.


Subproblem 1
x + -1.125 = 1.663016837

Simplifying
x + -1.125 = 1.663016837

Reorder the terms:
-1.125 + x = 1.663016837

Solving
-1.125 + x = 1.663016837

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 1.663016837 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.663016837 + 1.125
x = 1.663016837 + 1.125

Combine like terms: 1.663016837 + 1.125 = 2.788016837
x = 2.788016837

Simplifying
x = 2.788016837


Subproblem 2
x + -1.125 = -1.663016837

Simplifying
x + -1.125 = -1.663016837

Reorder the terms:
-1.125 + x = -1.663016837

Solving
-1.125 + x = -1.663016837

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -1.663016837 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.663016837 + 1.125
x = -1.663016837 + 1.125

Combine like terms: -1.663016837 + 1.125 = -0.538016837
x = -0.538016837

Simplifying
x = -0.538016837


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.788016837, -0.538016837}
Solution
x = {2.788016837, -0.538016837}

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