Basic Math Examples

$4 s - 5 s^{2} = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Let $u = s$ . Substitute $u$ for all occurrences of $s$ .

$4 u - 5 u^{2} = 0$

Step 1.2

Factor $u$ out of $4 u - 5 u^{2}$ .

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Step 1.2.1

Factor $u$ out of $4 u$ .

$u \cdot 4 - 5 u^{2} = 0$

Step 1.2.2

Factor $u$ out of $- 5 u^{2}$ .

$u \cdot 4 + u (- 5 u) = 0$

Step 1.2.3

Factor $u$ out of $u \cdot 4 + u (- 5 u)$ .

$u (4 - 5 u) = 0$

Step 1.3

Replace all occurrences of $u$ with $s$ .

$s (4 - 5 s) = 0$

Step 2

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

$s = 0$

$4 - 5 s = 0$

Step 3

Set $s$ equal to $0$ .

$s = 0$

Step 4

Set $4 - 5 s$ equal to $0$ and solve for $s$ .

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Step 4.1

Set $4 - 5 s$ equal to $0$ .

$4 - 5 s = 0$

Step 4.2

Solve $4 - 5 s = 0$ for $s$ .

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$- 5 s = - 4$

Step 4.2.2

Divide each term in $- 5 s = - 4$ by $- 5$ and simplify.

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Step 4.2.2.1

Divide each term in $- 5 s = - 4$ by $- 5$ .

$\frac{- 5 s}{- 5} = \frac{- 4}{- 5}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $- 5$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{- 5 s}{- 5} = \frac{- 4}{- 5}$

Step 4.2.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 4}{- 5}$

Step 4.2.2.3

Simplify the right side.

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Step 4.2.2.3.1

Dividing two negative values results in a positive value.

$s = \frac{4}{5}$

Step 5

The final solution is all the values that make $s (4 - 5 s) = 0$ true.

$s = 0, \frac{4}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$s = 0, \frac{4}{5}$

Decimal Form:

$s = 0, 0.8$