Solve for a j=(d^2-ah)/(3a)

$j = \frac{d^{2} - a h}{3 a}$

Rewrite the equation as $\frac{d^{2} - a h}{3 a} = j$ .

$\frac{d^{2} - a h}{3 a} = j$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 a, 1$

The LCM of one and any expression is the expression.

$3 a$

Multiply each term in $\frac{d^{2} - a h}{3 a} = j$ by $3 a$ to eliminate the fractions.

Multiply each term in $\frac{d^{2} - a h}{3 a} = j$ by $3 a$ .

$\frac{d^{2} - a h}{3 a} (3 a) = j (3 a)$

Simplify the left side.

Rewrite using the commutative property of multiplication.

$3 \frac{d^{2} - a h}{3 a} a = j (3 a)$

Cancel the common factor of $3$ .

Factor $3$ out of $3 a$ .

$3 \frac{d^{2} - a h}{3 (a)} a = j (3 a)$

Cancel the common factor.

$3 \frac{d^{2} - a h}{3 a} a = j (3 a)$

Rewrite the expression.

$\frac{d^{2} - a h}{a} a = j (3 a)$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{d^{2} - a h}{a} a = j (3 a)$

Rewrite the expression.

$d^{2} - a h = j (3 a)$

Simplify the right side.

Rewrite using the commutative property of multiplication.

$d^{2} - a h = 3 j a$

Solve the equation.

Subtract $3 j a$ from both sides of the equation.

$d^{2} - a h - 3 j a = 0$

Subtract $d^{2}$ from both sides of the equation.

$- a h - 3 j a = - d^{2}$

Factor $a$ out of $- a h - 3 j a$ .

Factor $a$ out of $- a h$ .

$a (- 1 h) - 3 j a = - d^{2}$

Factor $a$ out of $- 3 j a$ .

$a (- 1 h) + a (- 3 j) = - d^{2}$

Factor $a$ out of $a (- 1 h) + a (- 3 j)$ .

$a (- 1 h - 3 j) = - d^{2}$

Rewrite $- 1 h$ as $- h$ .

$a (- h - 3 j) = - d^{2}$

Divide each term in $a (- h - 3 j) = - d^{2}$ by $- h - 3 j$ and simplify.

Divide each term in $a (- h - 3 j) = - d^{2}$ by $- h - 3 j$ .

$\frac{a (- h - 3 j)}{- h - 3 j} = \frac{- d^{2}}{- h - 3 j}$

Simplify the left side.

Cancel the common factor of $- h - 3 j$ .

Cancel the common factor.

$\frac{a (- h - 3 j)}{- h - 3 j} = \frac{- d^{2}}{- h - 3 j}$

Divide $a$ by $1$ .

$a = \frac{- d^{2}}{- h - 3 j}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{d^{2}}{- h - 3 j}$

Factor $- 1$ out of $- h$ .

$a = - \frac{d^{2}}{- (h) - 3 j}$

Factor $- 1$ out of $- 3 j$ .

$a = - \frac{d^{2}}{- (h) - (3 j)}$

Factor $- 1$ out of $- (h) - (3 j)$ .

$a = - \frac{d^{2}}{- (h + 3 j)}$

Simplify the expression.

Rewrite $- (h + 3 j)$ as $- 1 (h + 3 j)$ .

$a = - \frac{d^{2}}{- 1 (h + 3 j)}$

Move the negative in front of the fraction.

$a = - - \frac{d^{2}}{h + 3 j}$

Multiply $- 1$ by $- 1$ .

$a = 1 \frac{d^{2}}{h + 3 j}$

Multiply $\frac{d^{2}}{h + 3 j}$ by $1$ .

$a = \frac{d^{2}}{h + 3 j}$

Solve for a j=(d^2-ah)/(3a)

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