(64x^2-240x+120)+(21x^2-140x+70)=0

Solution for (64x^2-240x+120)+(21x^2-140x+70)=0 equation:

Simplifying
(64x2 + -240x + 120) + (21x2 + -140x + 70) = 0

Reorder the terms:
(120 + -240x + 64x2) + (21x2 + -140x + 70) = 0

Remove parenthesis around (120 + -240x + 64x2)
120 + -240x + 64x2 + (21x2 + -140x + 70) = 0

Reorder the terms:
120 + -240x + 64x2 + (70 + -140x + 21x2) = 0

Remove parenthesis around (70 + -140x + 21x2)
120 + -240x + 64x2 + 70 + -140x + 21x2 = 0

Reorder the terms:
120 + 70 + -240x + -140x + 64x2 + 21x2 = 0

Combine like terms: 120 + 70 = 190
190 + -240x + -140x + 64x2 + 21x2 = 0

Combine like terms: -240x + -140x = -380x
190 + -380x + 64x2 + 21x2 = 0

Combine like terms: 64x2 + 21x2 = 85x2
190 + -380x + 85x2 = 0

Solving
190 + -380x + 85x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(38 + -76x + 17x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(38 + -76x + 17x2)' equal to zero and attempt to solve:

Simplifying
38 + -76x + 17x2 = 0

Solving
38 + -76x + 17x2 = 0

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

Divide each side by '17'.
2.235294118 + -4.470588235x + x2 = 0

Move the constant term to the right:

Add '-2.235294118' to each side of the equation.
2.235294118 + -4.470588235x + -2.235294118 + x2 = 0 + -2.235294118

Reorder the terms:
2.235294118 + -2.235294118 + -4.470588235x + x2 = 0 + -2.235294118

Combine like terms: 2.235294118 + -2.235294118 = 0.000000000
0.000000000 + -4.470588235x + x2 = 0 + -2.235294118
-4.470588235x + x2 = 0 + -2.235294118

Combine like terms: 0 + -2.235294118 = -2.235294118
-4.470588235x + x2 = -2.235294118

The x term is -4.470588235x.  Take half its coefficient (-2.235294118).
Square it (4.996539794) and add it to both sides.

Add '4.996539794' to each side of the equation.
-4.470588235x + 4.996539794 + x2 = -2.235294118 + 4.996539794

Reorder the terms:
4.996539794 + -4.470588235x + x2 = -2.235294118 + 4.996539794

Combine like terms: -2.235294118 + 4.996539794 = 2.761245676
4.996539794 + -4.470588235x + x2 = 2.761245676

Factor a perfect square on the left side:
(x + -2.235294118)(x + -2.235294118) = 2.761245676

Calculate the square root of the right side: 1.661699635

Break this problem into two subproblems by setting 
(x + -2.235294118) equal to 1.661699635 and -1.661699635.

Subproblem 1
x + -2.235294118 = 1.661699635

Simplifying
x + -2.235294118 = 1.661699635

Reorder the terms:
-2.235294118 + x = 1.661699635

Solving
-2.235294118 + x = 1.661699635

Solving for variable 'x'.

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

Add '2.235294118' to each side of the equation.
-2.235294118 + 2.235294118 + x = 1.661699635 + 2.235294118

Combine like terms: -2.235294118 + 2.235294118 = 0.000000000
0.000000000 + x = 1.661699635 + 2.235294118
x = 1.661699635 + 2.235294118

Combine like terms: 1.661699635 + 2.235294118 = 3.896993753
x = 3.896993753

Simplifying
x = 3.896993753

Subproblem 2
x + -2.235294118 = -1.661699635

Simplifying
x + -2.235294118 = -1.661699635

Reorder the terms:
-2.235294118 + x = -1.661699635

Solving
-2.235294118 + x = -1.661699635

Solving for variable 'x'.

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

Add '2.235294118' to each side of the equation.
-2.235294118 + 2.235294118 + x = -1.661699635 + 2.235294118

Combine like terms: -2.235294118 + 2.235294118 = 0.000000000
0.000000000 + x = -1.661699635 + 2.235294118
x = -1.661699635 + 2.235294118

Combine like terms: -1.661699635 + 2.235294118 = 0.573594483
x = 0.573594483

Simplifying
x = 0.573594483

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.896993753, 0.573594483}
Solution
x = {3.896993753, 0.573594483}