4(3x^2-18x+16)=0

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Solution for 4(3x^2-18x+16)=0 equation: 


Simplifying
4(3x2 + -18x + 16) = 0

Reorder the terms:
4(16 + -18x + 3x2) = 0
(16 * 4 + -18x * 4 + 3x2 * 4) = 0
(64 + -72x + 12x2) = 0

Solving
64 + -72x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -18x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(16 + -18x + 3x2)' equal to zero and attempt to solve:

Simplifying
16 + -18x + 3x2 = 0

Solving
16 + -18x + 3x2 = 0

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

Divide each side by '3'.
5.333333333 + -6x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -6x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -6x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -6x + x2 = 0 + -5.333333333
-6x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-6x + x2 = -5.333333333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -5.333333333 + 9

Reorder the terms:
9 + -6x + x2 = -5.333333333 + 9

Combine like terms: -5.333333333 + 9 = 3.666666667
9 + -6x + x2 = 3.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 3.666666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(x + -3) equal to 1.914854216 and -1.914854216.


Subproblem 1
x + -3 = 1.914854216

Simplifying
x + -3 = 1.914854216

Reorder the terms:
-3 + x = 1.914854216

Solving
-3 + x = 1.914854216

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 1.914854216 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.914854216 + 3
x = 1.914854216 + 3

Combine like terms: 1.914854216 + 3 = 4.914854216
x = 4.914854216

Simplifying
x = 4.914854216


Subproblem 2
x + -3 = -1.914854216

Simplifying
x + -3 = -1.914854216

Reorder the terms:
-3 + x = -1.914854216

Solving
-3 + x = -1.914854216

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -1.914854216 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.914854216 + 3
x = -1.914854216 + 3

Combine like terms: -1.914854216 + 3 = 1.085145784
x = 1.085145784

Simplifying
x = 1.085145784


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.914854216, 1.085145784}
Solution
x = {4.914854216, 1.085145784}

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