Finite Math Examples

$a^{2} + a b = a$

Step 1

Subtract $a$ from both sides of the equation.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Factor $a$ out of $a b$ .

$a \cdot a + a (b) - a = 0$

Step 2.3

Factor $a$ out of $- a$ .

$a \cdot a + a (b) + a \cdot - 1 = 0$

Step 2.4

Factor $a$ out of $a \cdot a + a (b)$ .

$a (a + b) + a \cdot - 1 = 0$

Step 2.5

Factor $a$ out of $a (a + b) + a \cdot - 1$ .

$a (a + b - 1) = 0$

Step 3

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

$a = 0$

$a + b - 1 = 0$

Step 4

Set $a$ equal to $0$ .

$a = 0$

Step 5

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

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Step 5.1

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

$a + b - 1 = 0$

Step 5.2

Move all terms not containing $a$ to the right side of the equation.

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Step 5.2.1

Subtract $b$ from both sides of the equation.

$a - 1 = - b$

Step 5.2.2

Add $1$ to both sides of the equation.

$a = - b + 1$

Step 6

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

$a = 0$

$a = - b + 1$