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

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


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

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

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

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

Combine like terms: -1xy + 30xy = 29xy
(29xy + 5x2 + -6y2) = 0

Solving
29xy + 5x2 + -6y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(5x + -1y)' equal to zero and attempt to solve:

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

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

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

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

Simplifying
x = 0.2y

Subproblem 2
Set the factor '(x + 6y)' equal to zero and attempt to solve:

Simplifying
x + 6y = 0

Solving
x + 6y = 0

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

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

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

Simplifying
x = -6y
Solution
x = {0.2y, -6y}

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