Y=(5n+2m)(a-b)-(a+b)(5n+2m)

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Solution for Y=(5n+2m)(a-b)-(a+b)(5n+2m) equation:


Simplifying
Y = (5n + 2m)(a + -1b) + -1(a + b)(5n + 2m)

Reorder the terms:
Y = (2m + 5n)(a + -1b) + -1(a + b)(5n + 2m)

Multiply (2m + 5n) * (a + -1b)
Y = (2m * (a + -1b) + 5n * (a + -1b)) + -1(a + b)(5n + 2m)
Y = ((a * 2m + -1b * 2m) + 5n * (a + -1b)) + -1(a + b)(5n + 2m)
Y = ((2am + -2bm) + 5n * (a + -1b)) + -1(a + b)(5n + 2m)
Y = (2am + -2bm + (a * 5n + -1b * 5n)) + -1(a + b)(5n + 2m)
Y = (2am + -2bm + (5an + -5bn)) + -1(a + b)(5n + 2m)

Reorder the terms:
Y = (2am + 5an + -2bm + -5bn) + -1(a + b)(5n + 2m)
Y = (2am + 5an + -2bm + -5bn) + -1(a + b)(5n + 2m)

Reorder the terms:
Y = 2am + 5an + -2bm + -5bn + -1(a + b)(2m + 5n)

Multiply (a + b) * (2m + 5n)
Y = 2am + 5an + -2bm + -5bn + -1(a(2m + 5n) + b(2m + 5n))
Y = 2am + 5an + -2bm + -5bn + -1((2m * a + 5n * a) + b(2m + 5n))
Y = 2am + 5an + -2bm + -5bn + -1((2am + 5an) + b(2m + 5n))
Y = 2am + 5an + -2bm + -5bn + -1(2am + 5an + (2m * b + 5n * b))
Y = 2am + 5an + -2bm + -5bn + -1(2am + 5an + (2bm + 5bn))
Y = 2am + 5an + -2bm + -5bn + -1(2am + 5an + 2bm + 5bn)
Y = 2am + 5an + -2bm + -5bn + (2am * -1 + 5an * -1 + 2bm * -1 + 5bn * -1)
Y = 2am + 5an + -2bm + -5bn + (-2am + -5an + -2bm + -5bn)

Reorder the terms:
Y = 2am + -2am + 5an + -5an + -2bm + -2bm + -5bn + -5bn

Combine like terms: 2am + -2am = 0
Y = 0 + 5an + -5an + -2bm + -2bm + -5bn + -5bn
Y = 5an + -5an + -2bm + -2bm + -5bn + -5bn

Combine like terms: 5an + -5an = 0
Y = 0 + -2bm + -2bm + -5bn + -5bn
Y = -2bm + -2bm + -5bn + -5bn

Combine like terms: -2bm + -2bm = -4bm
Y = -4bm + -5bn + -5bn

Combine like terms: -5bn + -5bn = -10bn
Y = -4bm + -10bn

Solving
Y = -4bm + -10bn

Solving for variable 'Y'.

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

Simplifying
Y = -4bm + -10bn

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