What is the answer to (x+m-n)^2-mx=nx+(x-2n)(x+2m) ?

The answer to (x+m-n)^2-mx=nx+(x-2n)(x+2m) is x=m+n;\quad m\ne-n

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(x+m-n)^2-mx=nx+(x-2n)(x+2m)

(x + m - n)^{2} - m x = n x + (x - 2 n) (x + 2 m)

x = m + n; m \neq = - n

Solution steps

(x + m - n)^{2} - m x = n x + (x - 2 n) (x + 2 m)

Expand

(x + m - n)^{2} - m x : x^{2} + m x - 2 n x + m^{2} + n^{2} - 2 mn

Expand

n x + (x - 2 n) (x + 2 m) : x^{2} + 2 m x - n x - 4 mn

x^{2} + m x - 2 n x + m^{2} + n^{2} - 2 mn = x^{2} + 2 m x - n x - 4 mn

Move

m^{2}

to the right side

x^{2} + m x - 2 n x + n^{2} - 2 mn = x^{2} + 2 m x - n x - 4 mn - m^{2}

Move

n^{2}

to the right side

x^{2} + m x - 2 n x - 2 mn = x^{2} + 2 m x - n x - 4 mn - m^{2} - n^{2}

Move

2 mn

to the right side

x^{2} + m x - 2 n x = x^{2} + 2 m x - n x - m^{2} - n^{2} - 2 mn

Subtract

x^{2} + 2 m x - n x

from both sides

x^{2} + m x - 2 n x - (x^{2} + 2 m x - n x) = x^{2} + 2 m x - n x - m^{2} - n^{2} - 2 mn - (x^{2} + 2 m x - n x)

Simplify

- m x - n x = - m^{2} - n^{2} - 2 mn

Factor

- m x - n x : - x (m + n)

- x (m + n) = - m^{2} - n^{2} - 2 mn

Divide both sides by

- (m + n); m \neq = - n

x = m + n; m \neq = - n

6 - 3 x = 27

2.1 x = 42

w, S = 2 (lw + l h + w h)

q, x^{2} - 2 q x - 3 x = - 5 q - 1

- 67 = 14 + 9 z

What is the answer to (x+m-n)^2-mx=nx+(x-2n)(x+2m) ?
The answer to (x+m-n)^2-mx=nx+(x-2n)(x+2m) is x=m+n;\quad m\ne-n