Pre-Algebra Examples

$5 w^{2} = 8 w$

Step 1

Subtract $8 w$ from both sides of the equation.

$5 w^{2} - 8 w = 0$

Step 2

Factor $w$ out of $5 w^{2} - 8 w$ .

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Step 2.1

Factor $w$ out of $5 w^{2}$ .

$w (5 w) - 8 w = 0$

Step 2.2

Factor $w$ out of $- 8 w$ .

$w (5 w) + w \cdot - 8 = 0$

Step 2.3

Factor $w$ out of $w (5 w) + w \cdot - 8$ .

$w (5 w - 8) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$w = 0$

$5 w - 8 = 0$

Step 4

Set $w$ equal to $0$ .

$w = 0$

Step 5

Set $5 w - 8$ equal to $0$ and solve for $w$ .

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Step 5.1

Set $5 w - 8$ equal to $0$ .

$5 w - 8 = 0$

Step 5.2

Solve $5 w - 8 = 0$ for $w$ .

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Step 5.2.1

Add $8$ to both sides of the equation.

$5 w = 8$

Step 5.2.2

Divide each term in $5 w = 8$ by $5$ and simplify.

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Step 5.2.2.1

Divide each term in $5 w = 8$ by $5$ .

$\frac{5 w}{5} = \frac{8}{5}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of $5$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{5 w}{5} = \frac{8}{5}$

Step 5.2.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{8}{5}$

Step 6

The final solution is all the values that make $w (5 w - 8) = 0$ true.

$w = 0, \frac{8}{5}$