Basic Math Examples

$a^{2} - 5 = a - 5$

Step 1

Subtract $a$ from both sides of the equation.

$a^{2} - 5 - a = - 5$

Step 2

Add $5$ to both sides of the equation.

$a^{2} - 5 - a + 5 = 0$

Step 3

Combine the opposite terms in $a^{2} - 5 - a + 5$ .

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Step 3.1

Add $- 5$ and $5$ .

$a^{2} - a + 0 = 0$

Step 3.2

Add $a^{2} - a$ and $0$ .

$a^{2} - a = 0$

Step 4

Factor $a$ out of $a^{2} - a$ .

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Step 4.1

Factor $a$ out of $a^{2}$ .

$a \cdot a - a = 0$

Step 4.2

Factor $a$ out of $- a$ .

$a \cdot a + a \cdot - 1 = 0$

Step 4.3

Factor $a$ out of $a \cdot a + a \cdot - 1$ .

$a (a - 1) = 0$

Step 5

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

$a = 0$

$a - 1 = 0$

Step 6

Set $a$ equal to $0$ .

$a = 0$

Step 7

Set $a - 1$ equal to $0$ and solve for $a$ .

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Step 7.1

Set $a - 1$ equal to $0$ .

$a - 1 = 0$

Step 7.2

Add $1$ to both sides of the equation.

$a = 1$

Step 8

The final solution is all the values that make $a (a - 1) = 0$ true.

$a = 0, 1$