Linear Algebra Examples

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

Step 1

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

$x = 0$

$4 x + 3 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

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

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Step 3.1

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

$4 x + 3 = 0$

Step 3.2

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

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Step 3.2.1

Subtract $3$ from both sides of the equation.

$4 x = - 3$

Step 3.2.2

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

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Step 3.2.2.1

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

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

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.2.3

Simplify the right side.

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Step 3.2.2.3.1

Move the negative in front of the fraction.

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

Step 4

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

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

Step 5

The domain is the set of all valid $x$ values.

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

Step 6