Algebra Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $u$ by $u$ .

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

Step 1.1.3

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

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

Step 1.2

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

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $u$ by $u$ .

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

Step 2.3

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Add $3 u$ and $0$ .

$3 u - 2 u = - 4$

Step 3.4

Subtract $2 u$ from $3 u$ .

$u = - 4$