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

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


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

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

Reorder the terms:
0 = ((32xy + 24x2) + 2y * (3x + 4y))
0 = ((32xy + 24x2) + 2y * (3x + 4y))
0 = (32xy + 24x2 + (3x * 2y + 4y * 2y))
0 = (32xy + 24x2 + (6xy + 8y2))

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

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

Solving
0 = 38xy + 24x2 + 8y2

Solving for variable 'x'.
Remove the zero:
-38xy + -24x2 + -8y2 = 38xy + 24x2 + 8y2 + -38xy + -24x2 + -8y2

Reorder the terms:
-38xy + -24x2 + -8y2 = 38xy + -38xy + 24x2 + -24x2 + 8y2 + -8y2

Combine like terms: 38xy + -38xy = 0
-38xy + -24x2 + -8y2 = 0 + 24x2 + -24x2 + 8y2 + -8y2
-38xy + -24x2 + -8y2 = 24x2 + -24x2 + 8y2 + -8y2

Combine like terms: 24x2 + -24x2 = 0
-38xy + -24x2 + -8y2 = 0 + 8y2 + -8y2
-38xy + -24x2 + -8y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
-38xy + -24x2 + -8y2 = 0

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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