=(7x-y)(x+2y)

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Solution for =(7x-y)(x+2y) equation: 


Simplifying
0 = (7x + -1y)(x + 2y)

Multiply (7x + -1y) * (x + 2y)
0 = (7x * (x + 2y) + -1y * (x + 2y))
0 = ((x * 7x + 2y * 7x) + -1y * (x + 2y))

Reorder the terms:
0 = ((14xy + 7x2) + -1y * (x + 2y))
0 = ((14xy + 7x2) + -1y * (x + 2y))
0 = (14xy + 7x2 + (x * -1y + 2y * -1y))
0 = (14xy + 7x2 + (-1xy + -2y2))

Reorder the terms:
0 = (14xy + -1xy + 7x2 + -2y2)

Combine like terms: 14xy + -1xy = 13xy
0 = (13xy + 7x2 + -2y2)

Solving
0 = 13xy + 7x2 + -2y2

Solving for variable 'x'.
Remove the zero:
-13xy + -7x2 + 2y2 = 13xy + 7x2 + -2y2 + -13xy + -7x2 + 2y2

Reorder the terms:
-13xy + -7x2 + 2y2 = 13xy + -13xy + 7x2 + -7x2 + -2y2 + 2y2

Combine like terms: 13xy + -13xy = 0
-13xy + -7x2 + 2y2 = 0 + 7x2 + -7x2 + -2y2 + 2y2
-13xy + -7x2 + 2y2 = 7x2 + -7x2 + -2y2 + 2y2

Combine like terms: 7x2 + -7x2 = 0
-13xy + -7x2 + 2y2 = 0 + -2y2 + 2y2
-13xy + -7x2 + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
-13xy + -7x2 + 2y2 = 0

Factor a trinomial.
(-1x + -2y)(7x + -1y) = 0


Subproblem 1
Set the factor '(-1x + -2y)' equal to zero and attempt to solve:

Simplifying
-1x + -2y = 0

Solving
-1x + -2y = 0

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

Add '2y' to each side of the equation.
-1x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
-1x + 0 = 0 + 2y
-1x = 0 + 2y
Remove the zero:
-1x = 2y

Divide each side by '-1'.
x = -2y

Simplifying
x = -2y

Subproblem 2
Set the factor '(7x + -1y)' equal to zero and attempt to solve:

Simplifying
7x + -1y = 0

Solving
7x + -1y = 0

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

Add 'y' to each side of the equation.
7x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
7x + 0 = 0 + y
7x = 0 + y
Remove the zero:
7x = y

Divide each side by '7'.
x = 0.1428571429y

Simplifying
x = 0.1428571429y
Solution
x = {-2y, 0.1428571429y}

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