(3x+4y)(8x+2y)=

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Solution for (3x+4y)(8x+2y)= equation: 


Simplifying
(3x + 4y)(8x + 2y) = 0

Multiply (3x + 4y) * (8x + 2y)
(3x * (8x + 2y) + 4y * (8x + 2y)) = 0
((8x * 3x + 2y * 3x) + 4y * (8x + 2y)) = 0

Reorder the terms:
((6xy + 24x2) + 4y * (8x + 2y)) = 0
((6xy + 24x2) + 4y * (8x + 2y)) = 0
(6xy + 24x2 + (8x * 4y + 2y * 4y)) = 0
(6xy + 24x2 + (32xy + 8y2)) = 0

Reorder the terms:
(6xy + 32xy + 24x2 + 8y2) = 0

Combine like terms: 6xy + 32xy = 38xy
(38xy + 24x2 + 8y2) = 0

Solving
38xy + 24x2 + 8y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(19xy + 12x2 + 4y2) = 0

Factor a trinomial.
2((4x + y)(3x + 4y)) = 0

Ignore the factor 2.

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 + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

Add '-4y' to each side of the equation.
3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
3x + 0 = 0 + -4y
3x = 0 + -4y
Remove the zero:
3x = -4y

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y
Solution
x = {-0.25y, -1.333333333y}

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