4(3x^2-20x+16)=0

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Solution for 4(3x^2-20x+16)=0 equation: 


Simplifying
4(3x2 + -20x + 16) = 0

Reorder the terms:
4(16 + -20x + 3x2) = 0
(16 * 4 + -20x * 4 + 3x2 * 4) = 0
(64 + -80x + 12x2) = 0

Solving
64 + -80x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -20x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(16 + -20x + 3x2)' equal to zero and attempt to solve:

Simplifying
16 + -20x + 3x2 = 0

Solving
16 + -20x + 3x2 = 0

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

Divide each side by '3'.
5.333333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -6.666666667x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -6.666666667x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -5.333333333
-6.666666667x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-6.666666667x + x2 = -5.333333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -5.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -5.333333333 + 11.11111112

Combine like terms: -5.333333333 + 11.11111112 = 5.777777787
11.11111112 + -6.666666667x + x2 = 5.777777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 5.777777787

Calculate the square root of the right side: 2.403700852

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.403700852 and -2.403700852.


Subproblem 1
x + -3.333333334 = 2.403700852

Simplifying
x + -3.333333334 = 2.403700852

Reorder the terms:
-3.333333334 + x = 2.403700852

Solving
-3.333333334 + x = 2.403700852

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 2.403700852 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 2.403700852 + 3.333333334
x = 2.403700852 + 3.333333334

Combine like terms: 2.403700852 + 3.333333334 = 5.737034186
x = 5.737034186

Simplifying
x = 5.737034186


Subproblem 2
x + -3.333333334 = -2.403700852

Simplifying
x + -3.333333334 = -2.403700852

Reorder the terms:
-3.333333334 + x = -2.403700852

Solving
-3.333333334 + x = -2.403700852

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -2.403700852 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -2.403700852 + 3.333333334
x = -2.403700852 + 3.333333334

Combine like terms: -2.403700852 + 3.333333334 = 0.929632482
x = 0.929632482

Simplifying
x = 0.929632482


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.737034186, 0.929632482}
Solution
x = {5.737034186, 0.929632482}

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