Finite Math Examples

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

Step 1

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

$x = 0$

$2 x - 3 = 0$

$3 x - 5 = 0$

$x + 4 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $2 x - 3$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Step 3.2

Solve $2 x - 3 = 0$ for $x$ .

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Step 3.2.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 3.2.2

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 3.2.2.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 4

Set $3 x - 5$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $3 x - 5$ equal to $0$ .

$3 x - 5 = 0$

Step 4.2

Solve $3 x - 5 = 0$ for $x$ .

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Step 4.2.1

Add $5$ to both sides of the equation.

$3 x = 5$

Step 4.2.2

Divide each term in $3 x = 5$ by $3$ and simplify.

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Step 4.2.2.1

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Step 4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Step 5

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

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Step 5.1

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

$x + 4 = 0$

Step 5.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 6

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

$x = 0, \frac{3}{2}, \frac{5}{3}, - 4$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{3}{2}, \frac{5}{3}, - 4$

Decimal Form:

$x = 0, 1.5, 1.\overline{6}, - 4$

Mixed Number Form:

$x = 0, 1 \frac{1}{2}, 1 \frac{2}{3}, - 4$