34(22x+24y)(32x+y)=

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Solution for 34(22x+24y)(32x+y)= equation: 


Simplifying
34(22x + 24y)(32x + y) = 0

Multiply (22x + 24y) * (32x + y)
34(22x * (32x + y) + 24y * (32x + y)) = 0
34((32x * 22x + y * 22x) + 24y * (32x + y)) = 0

Reorder the terms:
34((22xy + 704x2) + 24y * (32x + y)) = 0
34((22xy + 704x2) + 24y * (32x + y)) = 0
34(22xy + 704x2 + (32x * 24y + y * 24y)) = 0
34(22xy + 704x2 + (768xy + 24y2)) = 0

Reorder the terms:
34(22xy + 768xy + 704x2 + 24y2) = 0

Combine like terms: 22xy + 768xy = 790xy
34(790xy + 704x2 + 24y2) = 0
(790xy * 34 + 704x2 * 34 + 24y2 * 34) = 0
(26860xy + 23936x2 + 816y2) = 0

Solving
26860xy + 23936x2 + 816y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '68'.
68(395xy + 352x2 + 12y2) = 0

Factor a trinomial.
68((32x + y)(11x + 12y)) = 0

Ignore the factor 68.

Subproblem 1
Set the factor '(32x + y)' equal to zero and attempt to solve:

Simplifying
32x + y = 0

Solving
32x + y = 0

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

Add '-1y' to each side of the equation.
32x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
32x + 0 = 0 + -1y
32x = 0 + -1y
Remove the zero:
32x = -1y

Divide each side by '32'.
x = -0.03125y

Simplifying
x = -0.03125y

Subproblem 2
Set the factor '(11x + 12y)' equal to zero and attempt to solve:

Simplifying
11x + 12y = 0

Solving
11x + 12y = 0

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

Add '-12y' to each side of the equation.
11x + 12y + -12y = 0 + -12y

Combine like terms: 12y + -12y = 0
11x + 0 = 0 + -12y
11x = 0 + -12y
Remove the zero:
11x = -12y

Divide each side by '11'.
x = -1.090909091y

Simplifying
x = -1.090909091y
Solution
x = {-0.03125y, -1.090909091y}

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