(x-7y)(x+4y)=

Solution for (x-7y)(x+4y)= equation:

Simplifying
(x + -7y)(x + 4y) = 0

Multiply (x + -7y) * (x + 4y)
(x(x + 4y) + -7y * (x + 4y)) = 0
((x * x + 4y * x) + -7y * (x + 4y)) = 0

Reorder the terms:
((4xy + x2) + -7y * (x + 4y)) = 0
((4xy + x2) + -7y * (x + 4y)) = 0
(4xy + x2 + (x * -7y + 4y * -7y)) = 0
(4xy + x2 + (-7xy + -28y2)) = 0

Reorder the terms:
(4xy + -7xy + x2 + -28y2) = 0

Combine like terms: 4xy + -7xy = -3xy
(-3xy + x2 + -28y2) = 0

Solving
-3xy + x2 + -28y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -7y)(x + 4y) = 0

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

Simplifying
x + -7y = 0

Solving
x + -7y = 0

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

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

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

Simplifying
x = 7y
Subproblem 2
Set the factor '(x + 4y)' equal to zero and attempt to solve:

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

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

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

Simplifying
x = -4y
Solution
x = {7y, -4y}