Solve for u u(u-5)+8u=u(u+2)-4

$u (u - 5) + 8 u = u (u + 2) - 4$

Simplify $u (u - 5) + 8 u$ .

Simplify each term.

Apply the distributive property.

$u \cdot u + u \cdot - 5 + 8 u = u (u + 2) - 4$

Multiply $u$ by $u$ .

$u^{2} + u \cdot - 5 + 8 u = u (u + 2) - 4$

Move $- 5$ to the left of $u$ .

$u^{2} - 5 u + 8 u = u (u + 2) - 4$

Add $- 5 u$ and $8 u$ .

$u^{2} + 3 u = u (u + 2) - 4$

Simplify each term.

Apply the distributive property.

$u^{2} + 3 u = u \cdot u + u \cdot 2 - 4$

Multiply $u$ by $u$ .

$u^{2} + 3 u = u^{2} + u \cdot 2 - 4$

Move $2$ to the left of $u$ .

$u^{2} + 3 u = u^{2} + 2 u - 4$

Move all terms containing $u$ to the left side of the equation.

Subtract $u^{2}$ from both sides of the equation.

$u^{2} + 3 u - u^{2} = 2 u - 4$

Subtract $2 u$ from both sides of the equation.

$u^{2} + 3 u - u^{2} - 2 u = - 4$

Combine the opposite terms in $u^{2} + 3 u - u^{2} - 2 u$ .

Subtract $u^{2}$ from $u^{2}$ .

$3 u + 0 - 2 u = - 4$

Add $3 u$ and $0$ .

$3 u - 2 u = - 4$

Subtract $2 u$ from $3 u$ .

$u = - 4$