Solve for z a*(t+z)=45z+67

$a \cdot (t + z) = 45 z + 67$

Step 1

Simplify $a \cdot (t + z)$ .

Rewrite.

$0 + 0 + a \cdot (t + z) = 45 z + 67$

Simplify by adding zeros.

$a \cdot (t + z) = 45 z + 67$

Apply the distributive property.

$a t + a z = 45 z + 67$

Step 2

Subtract $45 z$ from both sides of the equation.

$a t + a z - 45 z = 67$

Step 3

Subtract $a t$ from both sides of the equation.

$a z - 45 z = 67 - a t$

Step 4

Factor $z$ out of $a z - 45 z$ .

Factor $z$ out of $a z$ .

$z a - 45 z = 67 - a t$

Factor $z$ out of $- 45 z$ .

$z a + z \cdot - 45 = 67 - a t$

Factor $z$ out of $z a + z \cdot - 45$ .

$z (a - 45) = 67 - a t$

Step 5

Divide each term in $z (a - 45) = 67 - a t$ by $a - 45$ and simplify.

Divide each term in $z (a - 45) = 67 - a t$ by $a - 45$ .

$\frac{z (a - 45)}{a - 45} = \frac{67}{a - 45} + \frac{- a t}{a - 45}$

Simplify the left side.

Cancel the common factor of $a - 45$ .

Cancel the common factor.

$\frac{z (a - 45)}{a - 45} = \frac{67}{a - 45} + \frac{- a t}{a - 45}$

Divide $z$ by $1$ .

$z = \frac{67}{a - 45} + \frac{- a t}{a - 45}$

Simplify the right side.

Combine the numerators over the common denominator.

$z = \frac{67 - a t}{a - 45}$