(21x+7y)(4x+y)=

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Solution for (21x+7y)(4x+y)= equation: 


Simplifying
(21x + 7y)(4x + y) = 0

Multiply (21x + 7y) * (4x + y)
(21x * (4x + y) + 7y * (4x + y)) = 0
((4x * 21x + y * 21x) + 7y * (4x + y)) = 0

Reorder the terms:
((21xy + 84x2) + 7y * (4x + y)) = 0
((21xy + 84x2) + 7y * (4x + y)) = 0
(21xy + 84x2 + (4x * 7y + y * 7y)) = 0
(21xy + 84x2 + (28xy + 7y2)) = 0

Reorder the terms:
(21xy + 28xy + 84x2 + 7y2) = 0

Combine like terms: 21xy + 28xy = 49xy
(49xy + 84x2 + 7y2) = 0

Solving
49xy + 84x2 + 7y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(7xy + 12x2 + y2) = 0

Factor a trinomial.
7((4x + y)(3x + y)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(4x + y)' equal to zero and attempt to solve:

Simplifying
4x + y = 0

Solving
4x + y = 0

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

Add '-1y' to each side of the equation.
4x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
4x + 0 = 0 + -1y
4x = 0 + -1y
Remove the zero:
4x = -1y

Divide each side by '4'.
x = -0.25y

Simplifying
x = -0.25y

Subproblem 2
Set the factor '(3x + y)' equal to zero and attempt to solve:

Simplifying
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y
Solution
x = {-0.25y, -0.3333333333y}

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