Y=(6x-5y)(3x-10y)-(2x+7y)(9x+4y)

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Solution for Y=(6x-5y)(3x-10y)-(2x+7y)(9x+4y) equation: 


Simplifying
Y = (6x + -5y)(3x + -10y) + -1(2x + 7y)(9x + 4y)

Multiply (6x + -5y) * (3x + -10y)
Y = (6x * (3x + -10y) + -5y * (3x + -10y)) + -1(2x + 7y)(9x + 4y)
Y = ((3x * 6x + -10y * 6x) + -5y * (3x + -10y)) + -1(2x + 7y)(9x + 4y)

Reorder the terms:
Y = ((-60xy + 18x2) + -5y * (3x + -10y)) + -1(2x + 7y)(9x + 4y)
Y = ((-60xy + 18x2) + -5y * (3x + -10y)) + -1(2x + 7y)(9x + 4y)
Y = (-60xy + 18x2 + (3x * -5y + -10y * -5y)) + -1(2x + 7y)(9x + 4y)
Y = (-60xy + 18x2 + (-15xy + 50y2)) + -1(2x + 7y)(9x + 4y)

Reorder the terms:
Y = (-60xy + -15xy + 18x2 + 50y2) + -1(2x + 7y)(9x + 4y)

Combine like terms: -60xy + -15xy = -75xy
Y = (-75xy + 18x2 + 50y2) + -1(2x + 7y)(9x + 4y)

Multiply (2x + 7y) * (9x + 4y)
Y = -75xy + 18x2 + 50y2 + -1(2x * (9x + 4y) + 7y * (9x + 4y))
Y = -75xy + 18x2 + 50y2 + -1((9x * 2x + 4y * 2x) + 7y * (9x + 4y))

Reorder the terms:
Y = -75xy + 18x2 + 50y2 + -1((8xy + 18x2) + 7y * (9x + 4y))
Y = -75xy + 18x2 + 50y2 + -1((8xy + 18x2) + 7y * (9x + 4y))
Y = -75xy + 18x2 + 50y2 + -1(8xy + 18x2 + (9x * 7y + 4y * 7y))
Y = -75xy + 18x2 + 50y2 + -1(8xy + 18x2 + (63xy + 28y2))

Reorder the terms:
Y = -75xy + 18x2 + 50y2 + -1(8xy + 63xy + 18x2 + 28y2)

Combine like terms: 8xy + 63xy = 71xy
Y = -75xy + 18x2 + 50y2 + -1(71xy + 18x2 + 28y2)
Y = -75xy + 18x2 + 50y2 + (71xy * -1 + 18x2 * -1 + 28y2 * -1)
Y = -75xy + 18x2 + 50y2 + (-71xy + -18x2 + -28y2)

Reorder the terms:
Y = -75xy + -71xy + 18x2 + -18x2 + 50y2 + -28y2

Combine like terms: -75xy + -71xy = -146xy
Y = -146xy + 18x2 + -18x2 + 50y2 + -28y2

Combine like terms: 18x2 + -18x2 = 0
Y = -146xy + 0 + 50y2 + -28y2
Y = -146xy + 50y2 + -28y2

Combine like terms: 50y2 + -28y2 = 22y2
Y = -146xy + 22y2

Solving
Y = -146xy + 22y2

Solving for variable 'Y'.

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

Simplifying
Y = -146xy + 22y2

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