3x(4x+11y)-8y(4x+11y)=0

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Solution for 3x(4x+11y)-8y(4x+11y)=0 equation: 


Simplifying
3x(4x + 11y) + -8y(4x + 11y) = 0
(4x * 3x + 11y * 3x) + -8y(4x + 11y) = 0

Reorder the terms:
(33xy + 12x2) + -8y(4x + 11y) = 0
(33xy + 12x2) + -8y(4x + 11y) = 0
33xy + 12x2 + (4x * -8y + 11y * -8y) = 0
33xy + 12x2 + (-32xy + -88y2) = 0

Reorder the terms:
33xy + -32xy + 12x2 + -88y2 = 0

Combine like terms: 33xy + -32xy = 1xy
1xy + 12x2 + -88y2 = 0

Solving
1xy + 12x2 + -88y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -8y)(4x + 11y) = 0


Subproblem 1
Set the factor '(3x + -8y)' equal to zero and attempt to solve:

Simplifying
3x + -8y = 0

Solving
3x + -8y = 0

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

Add '8y' to each side of the equation.
3x + -8y + 8y = 0 + 8y

Combine like terms: -8y + 8y = 0
3x + 0 = 0 + 8y
3x = 0 + 8y
Remove the zero:
3x = 8y

Divide each side by '3'.
x = 2.666666667y

Simplifying
x = 2.666666667y

Subproblem 2
Set the factor '(4x + 11y)' equal to zero and attempt to solve:

Simplifying
4x + 11y = 0

Solving
4x + 11y = 0

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

Add '-11y' to each side of the equation.
4x + 11y + -11y = 0 + -11y

Combine like terms: 11y + -11y = 0
4x + 0 = 0 + -11y
4x = 0 + -11y
Remove the zero:
4x = -11y

Divide each side by '4'.
x = -2.75y

Simplifying
x = -2.75y
Solution
x = {2.666666667y, -2.75y}

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