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

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


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

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

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

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

Combine like terms: -4xy + xy = -3xy
4(-3xy + x2 + -4y2) = 0
(-3xy * 4 + x2 * 4 + -4y2 * 4) = 0
(-12xy + 4x2 + -16y2) = 0

Solving
-12xy + 4x2 + -16y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3xy + x2 + -4y2) = 0

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

Ignore the factor 4.

Subproblem 1
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

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {4y, -1y}

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