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 = 4am
y = 4am + 5an + -5an + -2bm + 2bm + -5bn + -5bn

Combine like terms: 5an + -5an = 0
y = 4am + 0 + -2bm + 2bm + -5bn + -5bn
y = 4am + -2bm + 2bm + -5bn + -5bn

Combine like terms: -2bm + 2bm = 0
y = 4am + 0 + -5bn + -5bn
y = 4am + -5bn + -5bn

Combine like terms: -5bn + -5bn = -10bn
y = 4am + -10bn

Solving
y = 4am + -10bn

Solving for variable 'y'.

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

Simplifying
y = 4am + -10bn

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