4((3x^2)-21x+26)=0

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Solution for 4((3x^2)-21x+26)=0 equation: 


Simplifying
4((3x2) + -21x + 26) = 0

Reorder the terms:
4(26 + -21x + (3x2)) = 0
(26 * 4 + -21x * 4 + (3x2) * 4) = 0
(104 + -84x + 12x2) = 0

Solving
104 + -84x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(26 + -21x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(26 + -21x + 3x2)' equal to zero and attempt to solve:

Simplifying
26 + -21x + 3x2 = 0

Solving
26 + -21x + 3x2 = 0

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

Divide each side by '3'.
8.666666667 + -7x + x2 = 0

Move the constant term to the right:

Add '-8.666666667' to each side of the equation.
8.666666667 + -7x + -8.666666667 + x2 = 0 + -8.666666667

Reorder the terms:
8.666666667 + -8.666666667 + -7x + x2 = 0 + -8.666666667

Combine like terms: 8.666666667 + -8.666666667 = 0.000000000
0.000000000 + -7x + x2 = 0 + -8.666666667
-7x + x2 = 0 + -8.666666667

Combine like terms: 0 + -8.666666667 = -8.666666667
-7x + x2 = -8.666666667

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -8.666666667 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -8.666666667 + 12.25

Combine like terms: -8.666666667 + 12.25 = 3.583333333
12.25 + -7x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + -3.5) equal to 1.892969449 and -1.892969449.


Subproblem 1
x + -3.5 = 1.892969449

Simplifying
x + -3.5 = 1.892969449

Reorder the terms:
-3.5 + x = 1.892969449

Solving
-3.5 + x = 1.892969449

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 1.892969449 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 1.892969449 + 3.5
x = 1.892969449 + 3.5

Combine like terms: 1.892969449 + 3.5 = 5.392969449
x = 5.392969449

Simplifying
x = 5.392969449


Subproblem 2
x + -3.5 = -1.892969449

Simplifying
x + -3.5 = -1.892969449

Reorder the terms:
-3.5 + x = -1.892969449

Solving
-3.5 + x = -1.892969449

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -1.892969449 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -1.892969449 + 3.5
x = -1.892969449 + 3.5

Combine like terms: -1.892969449 + 3.5 = 1.607030551
x = 1.607030551

Simplifying
x = 1.607030551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.392969449, 1.607030551}
Solution
x = {5.392969449, 1.607030551}

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