What is the answer to acx-bxd+d^3=c^3+adx-bcx ?

The answer to acx-bxd+d^3=c^3+adx-bcx is x=(c^2+cd+d^2)/(a+b);\quad a\ne-b

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acx-bxd+d^3=c^3+adx-bcx

a c x - b x d + d^{3} = c^{3} + a d x - b c x

x = \frac{c ^{2} + c d + d ^{2}}{a + b}; a \neq = - b

Solution steps

a c x - b x d + d^{3} = c^{3} + a d x - b c x

Move

d^{3}

to the right side

a c x - b x d = c^{3} + a d x - b c x - d^{3}

Subtract

a d x - b c x

from both sides

a c x - b x d - (a d x - b c x) = c^{3} + a d x - b c x - d^{3} - (a d x - b c x)

Simplify

a c x - b d x - a d x + c b x = c^{3} - d^{3}

Factor

a c x - b d x - a d x + c b x : x (c - d) (a + b)

x (c - d) (a + b) = c^{3} - d^{3}

Divide both sides by

(c - d) (a + b); a \neq = - b

x = \frac{c ^{2} + c d + d ^{2}}{a + b}; a \neq = - b

y = \frac{2 y + 1}{5}

- 3 + 2 (n - 1) = - 20 + 5 n

2 x - 5 = 4 x + 7

- \frac{5}{2} a + \frac{4}{3} + \frac{2}{3} = \frac{13}{4}

y, x^{2} + 4 x y = 1200

What is the answer to acx-bxd+d^3=c^3+adx-bcx ?
The answer to acx-bxd+d^3=c^3+adx-bcx is x=(c^2+cd+d^2)/(a+b);\quad a\ne-b