2n(m-n)+(m-n)(m-n)=

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Solution for 2n(m-n)+(m-n)(m-n)= equation:


Simplifying
2n(m + -1n) + (m + -1n)(m + -1n) = 0
(m * 2n + -1n * 2n) + (m + -1n)(m + -1n) = 0
(2mn + -2n2) + (m + -1n)(m + -1n) = 0

Multiply (m + -1n) * (m + -1n)
2mn + -2n2 + (m(m + -1n) + -1n * (m + -1n)) = 0
2mn + -2n2 + ((m * m + -1n * m) + -1n * (m + -1n)) = 0

Reorder the terms:
2mn + -2n2 + ((-1mn + m2) + -1n * (m + -1n)) = 0
2mn + -2n2 + ((-1mn + m2) + -1n * (m + -1n)) = 0
2mn + -2n2 + (-1mn + m2 + (m * -1n + -1n * -1n)) = 0
2mn + -2n2 + (-1mn + m2 + (-1mn + 1n2)) = 0

Reorder the terms:
2mn + -2n2 + (-1mn + -1mn + m2 + 1n2) = 0

Combine like terms: -1mn + -1mn = -2mn
2mn + -2n2 + (-2mn + m2 + 1n2) = 0

Reorder the terms:
2mn + -2mn + m2 + -2n2 + 1n2 = 0

Combine like terms: 2mn + -2mn = 0
0 + m2 + -2n2 + 1n2 = 0
m2 + -2n2 + 1n2 = 0

Combine like terms: -2n2 + 1n2 = -1n2
m2 + -1n2 = 0

Solving
m2 + -1n2 = 0

Solving for variable 'm'.

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

Add 'n2' to each side of the equation.
m2 + -1n2 + n2 = 0 + n2

Combine like terms: -1n2 + n2 = 0
m2 + 0 = 0 + n2
m2 = 0 + n2
Remove the zero:
m2 = n2

Simplifying
m2 = n2

Take the square root of each side:
m = {-1n, n}

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