Algebra Examples

$y = (x + 3) (x - 5) (x - 6)$

Step 1

Set $(x + 3) (x - 5) (x - 6)$ equal to $0$ .

$(x + 3) (x - 5) (x - 6) = 0$

Step 2

Solve for $x$ .

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Step 2.1

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

$x + 3 = 0$

$x - 5 = 0$

$x - 6 = 0$

Step 2.2

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 2.2.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 2.3

Set $x - 5$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 2.3.2

Add $5$ to both sides of the equation.

$x = 5$

Step 2.4

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 2.4.2

Add $6$ to both sides of the equation.

$x = 6$

Step 2.5

The final solution is all the values that make $(x + 3) (x - 5) (x - 6) = 0$ true.

$x = - 3, 5, 6$

Step 3