Basic Math Examples

$(4 z + 3) (4 - z) = 0$

Step 1

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

$4 z + 3 = 0$

$4 - z = 0$

Step 2

Set $4 z + 3$ equal to $0$ and solve for $z$ .

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Step 2.1

Set $4 z + 3$ equal to $0$ .

$4 z + 3 = 0$

Step 2.2

Solve $4 z + 3 = 0$ for $z$ .

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Step 2.2.1

Subtract $3$ from both sides of the equation.

$4 z = - 3$

Step 2.2.2

Divide each term in $4 z = - 3$ by $4$ and simplify.

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Step 2.2.2.1

Divide each term in $4 z = - 3$ by $4$ .

$\frac{4 z}{4} = \frac{- 3}{4}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{4 z}{4} = \frac{- 3}{4}$

Step 2.2.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 3}{4}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Move the negative in front of the fraction.

$z = - \frac{3}{4}$

Step 3

Set $4 - z$ equal to $0$ and solve for $z$ .

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Step 3.1

Set $4 - z$ equal to $0$ .

$4 - z = 0$

Step 3.2

Solve $4 - z = 0$ for $z$ .

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$- z = - 4$

Step 3.2.2

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

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Step 3.2.2.1

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

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

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2.2.2

Divide $z$ by $1$ .

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

Step 3.2.2.3

Simplify the right side.

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Step 3.2.2.3.1

Divide $- 4$ by $- 1$ .

$z = 4$

Step 4

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

$z = - \frac{3}{4}, 4$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{3}{4}, 4$

Decimal Form:

$z = - 0.75, 4$