Algebra Examples

$f (x) = (10 x - 3) (4 x + 1) (5 x - 2)$

Step 1

Set $(10 x - 3) (4 x + 1) (5 x - 2)$ equal to $0$ .

$(10 x - 3) (4 x + 1) (5 x - 2) = 0$

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 $0$ .

$10 x - 3 = 0$

$4 x + 1 = 0$

$5 x - 2 = 0$

Step 2.2

Set $10 x - 3$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $10 x - 3$ equal to $0$ .

$10 x - 3 = 0$

Step 2.2.2

Solve $10 x - 3 = 0$ for $x$ .

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Step 2.2.2.1

Add $3$ to both sides of the equation.

$10 x = 3$

Step 2.2.2.2

Divide each term in $10 x = 3$ by $10$ and simplify.

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Step 2.2.2.2.1

Divide each term in $10 x = 3$ by $10$ .

$\frac{10 x}{10} = \frac{3}{10}$

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 $10$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{3}{10}$

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{10}$

Step 2.3

Set $4 x + 1$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $4 x + 1$ equal to $0$ .

$4 x + 1 = 0$

Step 2.3.2

Solve $4 x + 1 = 0$ for $x$ .

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Step 2.3.2.1

Subtract $1$ from both sides of the equation.

$4 x = - 1$

Step 2.3.2.2

Divide each term in $4 x = - 1$ by $4$ and simplify.

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Step 2.3.2.2.1

Divide each term in $4 x = - 1$ by $4$ .

$\frac{4 x}{4} = \frac{- 1}{4}$

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 $4$ .

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Step 2.3.2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 1}{4}$

Step 2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{4}$

Step 2.3.2.2.3

Simplify the right side.

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Step 2.3.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{4}$

Step 2.4

Set $5 x - 2$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $5 x - 2$ equal to $0$ .

$5 x - 2 = 0$

Step 2.4.2

Solve $5 x - 2 = 0$ for $x$ .

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Step 2.4.2.1

Add $2$ to both sides of the equation.

$5 x = 2$

Step 2.4.2.2

Divide each term in $5 x = 2$ by $5$ and simplify.

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Step 2.4.2.2.1

Divide each term in $5 x = 2$ by $5$ .

$\frac{5 x}{5} = \frac{2}{5}$

Step 2.4.2.2.2

Simplify the left side.

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Step 2.4.2.2.2.1

Cancel the common factor of $5$ .

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Step 2.4.2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{2}{5}$

Step 2.4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{5}$

Step 2.5

The final solution is all the values that make $(10 x - 3) (4 x + 1) (5 x - 2) = 0$ true.

$x = \frac{3}{10}, - \frac{1}{4}, \frac{2}{5}$

Step 3