Algebra Examples

$p (x) = (2 x - 6) (8 x - 1) (x - 5)$

Step 1

Set $(2 x - 6) (8 x - 1) (x - 5)$ equal to $0$ .

$(2 x - 6) (8 x - 1) (x - 5) = 0$

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 $0$ .

$2 x - 6 = 0$

$8 x - 1 = 0$

$x - 5 = 0$

Step 2.2

Set $2 x - 6$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $2 x - 6$ equal to $0$ .

$2 x - 6 = 0$

Step 2.2.2

Solve $2 x - 6 = 0$ for $x$ .

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Step 2.2.2.1

Add $6$ to both sides of the equation.

$2 x = 6$

Step 2.2.2.2

Divide each term in $2 x = 6$ by $2$ and simplify.

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Step 2.2.2.2.1

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Divide $6$ by $2$ .

$x = 3$

Step 2.3

Set $8 x - 1$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $8 x - 1$ equal to $0$ .

$8 x - 1 = 0$

Step 2.3.2

Solve $8 x - 1 = 0$ for $x$ .

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Step 2.3.2.1

Add $1$ to both sides of the equation.

$8 x = 1$

Step 2.3.2.2

Divide each term in $8 x = 1$ by $8$ and simplify.

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Step 2.3.2.2.1

Divide each term in $8 x = 1$ by $8$ .

$\frac{8 x}{8} = \frac{1}{8}$

Step 2.3.2.2.2

Simplify the left side.

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Step 2.3.2.2.2.1

Cancel the common factor of $8$ .

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Step 2.3.2.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{1}{8}$

Step 2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{8}$

Step 2.4

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

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Step 2.4.1

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

$x - 5 = 0$

Step 2.4.2

Add $5$ to both sides of the equation.

$x = 5$

Step 2.5

The final solution is all the values that make $(2 x - 6) (8 x - 1) (x - 5) = 0$ true.

$x = 3, \frac{1}{8}, 5$

Step 3