Basic Math Examples

$g (g (- 3)) = g ({(- 3)}^{2} - 4 \cdot - 3 - 5)$

Step 1

Simplify $g (g (- 3))$ .

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Step 1.1

Rewrite using the commutative property of multiplication.

$- 3 g \cdot g = g ({(- 3)}^{2} - 4 \cdot - 3 - 5)$

Step 1.2

Multiply $g$ by $g$ by adding the exponents.

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Step 1.2.1

Move $g$ .

$- 3 (g \cdot g) = g ({(- 3)}^{2} - 4 \cdot - 3 - 5)$

Step 1.2.2

Multiply $g$ by $g$ .

$- 3 g^{2} = g ({(- 3)}^{2} - 4 \cdot - 3 - 5)$

Step 2

Simplify $g ({(- 3)}^{2} - 4 \cdot - 3 - 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $- 3$ to the power of $2$ .

$- 3 g^{2} = g (9 - 4 \cdot - 3 - 5)$

Step 2.1.2

Multiply $- 4$ by $- 3$ .

$- 3 g^{2} = g (9 + 12 - 5)$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $9$ and $12$ .

$- 3 g^{2} = g (21 - 5)$

Step 2.2.2

Subtract $5$ from $21$ .

$- 3 g^{2} = g \cdot 16$

Step 2.2.3

Move $16$ to the left of $g$ .

$- 3 g^{2} = 16 g$

Step 3

Subtract $16 g$ from both sides of the equation.

$- 3 g^{2} - 16 g = 0$

Step 4

Factor $- g$ out of $- 3 g^{2} - 16 g$ .

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Step 4.1

Factor $- g$ out of $- 3 g^{2}$ .

$- g (3 g) - 16 g = 0$

Step 4.2

Factor $- g$ out of $- 16 g$ .

$- g (3 g) - g \cdot 16 = 0$

Step 4.3

Factor $- g$ out of $- g (3 g) - g (16)$ .

$- g (3 g + 16) = 0$

Step 5

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

$g = 0$

$3 g + 16 = 0$

Step 6

Set $g$ equal to $0$ .

$g = 0$

Step 7

Set $3 g + 16$ equal to $0$ and solve for $g$ .

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Step 7.1

Set $3 g + 16$ equal to $0$ .

$3 g + 16 = 0$

Step 7.2

Solve $3 g + 16 = 0$ for $g$ .

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Step 7.2.1

Subtract $16$ from both sides of the equation.

$3 g = - 16$

Step 7.2.2

Divide each term in $3 g = - 16$ by $3$ and simplify.

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Step 7.2.2.1

Divide each term in $3 g = - 16$ by $3$ .

$\frac{3 g}{3} = \frac{- 16}{3}$

Step 7.2.2.2

Simplify the left side.

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Step 7.2.2.2.1

Cancel the common factor of $3$ .

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Step 7.2.2.2.1.1

Cancel the common factor.

$\frac{3 g}{3} = \frac{- 16}{3}$

Step 7.2.2.2.1.2

Divide $g$ by $1$ .

$g = \frac{- 16}{3}$

Step 7.2.2.3

Simplify the right side.

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Step 7.2.2.3.1

Move the negative in front of the fraction.

$g = - \frac{16}{3}$

Step 8

The final solution is all the values that make $- g (3 g + 16) = 0$ true.

$g = 0, - \frac{16}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$g = 0, - \frac{16}{3}$

Decimal Form:

$g = 0, - 5.\overline{3}$

Mixed Number Form:

$g = 0, - 5 \frac{1}{3}$