Finite Math Examples

$f (x) = 4 x + 4 x^{2}$

Step 1

Set $4 x + 4 x^{2}$ equal to $0$ .

$4 x + 4 x^{2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor the left side of the equation.

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Step 2.1.1

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$4 u + 4 u^{2} = 0$

Step 2.1.2

Factor $4 u$ out of $4 u + 4 u^{2}$ .

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Step 2.1.2.1

Factor $4 u$ out of $4 u$ .

$4 u (1) + 4 u^{2} = 0$

Step 2.1.2.2

Factor $4 u$ out of $4 u^{2}$ .

$4 u (1) + 4 u (u) = 0$

Step 2.1.2.3

Factor $4 u$ out of $4 u (1) + 4 u (u)$ .

$4 u (1 + u) = 0$

Step 2.1.3

Replace all occurrences of $u$ with $x$ .

$4 x (1 + x) = 0$

Step 2.2

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

$x = 0$

$1 + x = 0$

Step 2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.4

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

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Step 2.4.1

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

$1 + x = 0$

Step 2.4.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.5

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

$x = 0, - 1$

Step 3