(5x+y)(6x-y)=0

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Solution for (5x+y)(6x-y)=0 equation: 


Simplifying
(5x + y)(6x + -1y) = 0

Multiply (5x + y) * (6x + -1y)
(5x * (6x + -1y) + y(6x + -1y)) = 0
((6x * 5x + -1y * 5x) + y(6x + -1y)) = 0

Reorder the terms:
((-5xy + 30x2) + y(6x + -1y)) = 0
((-5xy + 30x2) + y(6x + -1y)) = 0
(-5xy + 30x2 + (6x * y + -1y * y)) = 0
(-5xy + 30x2 + (6xy + -1y2)) = 0

Reorder the terms:
(-5xy + 6xy + 30x2 + -1y2) = 0

Combine like terms: -5xy + 6xy = 1xy
(1xy + 30x2 + -1y2) = 0

Solving
1xy + 30x2 + -1y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + -1y)(5x + y) = 0


Subproblem 1
Set the factor '(6x + -1y)' equal to zero and attempt to solve:

Simplifying
6x + -1y = 0

Solving
6x + -1y = 0

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

Add 'y' to each side of the equation.
6x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
6x + 0 = 0 + y
6x = 0 + y
Remove the zero:
6x = y

Divide each side by '6'.
x = 0.1666666667y

Simplifying
x = 0.1666666667y

Subproblem 2
Set the factor '(5x + y)' equal to zero and attempt to solve:

Simplifying
5x + y = 0

Solving
5x + y = 0

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

Add '-1y' to each side of the equation.
5x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
5x + 0 = 0 + -1y
5x = 0 + -1y
Remove the zero:
5x = -1y

Divide each side by '5'.
x = -0.2y

Simplifying
x = -0.2y
Solution
x = {0.1666666667y, -0.2y}

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