Solve for x f(x+3)=f(x+1)+4x+12

$f (x + 3) = f (x + 1) + 4 x + 12$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$f (x + 1) + 4 x + 12 = f (x + 3)$

Step 2

Simplify each term.

Apply the distributive property.

$f x + f \cdot 1 + 4 x + 12 = f (x + 3)$

Multiply $f$ by $1$ .

$f x + f + 4 x + 12 = f (x + 3)$

Step 3

Simplify $f (x + 3)$ .

Apply the distributive property.

$f x + f + 4 x + 12 = f x + f \cdot 3$

Move $3$ to the left of $f$ .

$f x + f + 4 x + 12 = f x + 3 f$

Step 4

Move all terms containing $x$ to the left side of the equation.

Subtract $f x$ from both sides of the equation.

$f x + f + 4 x + 12 - f x = 3 f$

Combine the opposite terms in $f x + f + 4 x + 12 - f x$ .

Subtract $f x$ from $f x$ .

$f + 4 x + 12 + 0 = 3 f$

Add $f + 4 x + 12$ and $0$ .

$f + 4 x + 12 = 3 f$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Subtract $f$ from both sides of the equation.

$4 x + 12 = 3 f - f$

Subtract $12$ from both sides of the equation.

$4 x = 3 f - f - 12$

Subtract $f$ from $3 f$ .

$4 x = 2 f - 12$

Step 6

Divide each term in $4 x = 2 f - 12$ by $4$ and simplify.

Divide each term in $4 x = 2 f - 12$ by $4$ .

$\frac{4 x}{4} = \frac{2 f}{4} + \frac{- 12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{2 f}{4} + \frac{- 12}{4}$

Divide $x$ by $1$ .

$x = \frac{2 f}{4} + \frac{- 12}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 f$ .

$x = \frac{2 (f)}{4} + \frac{- 12}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 f}{2 \cdot 2} + \frac{- 12}{4}$

Cancel the common factor.

$x = \frac{2 f}{2 \cdot 2} + \frac{- 12}{4}$

Rewrite the expression.

$x = \frac{f}{2} + \frac{- 12}{4}$

Divide $- 12$ by $4$ .

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

Solve for x f(x+3)=f(x+1)+4x+12

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