Solve for t 5t+3=4w(t+2)

$5 t + 3 = 4 w (t + 2)$

Step 1

Simplify $4 w (t + 2)$ .

Rewrite.

$5 t + 3 = 0 + 0 + 4 w (t + 2)$

Simplify by adding zeros.

$5 t + 3 = 4 w (t + 2)$

Apply the distributive property.

$5 t + 3 = 4 w t + 4 w \cdot 2$

Multiply $2$ by $4$ .

$5 t + 3 = 4 w t + 8 w$

Step 2

Subtract $4 w t$ from both sides of the equation.

$5 t + 3 - 4 w t = 8 w$

Step 3

Subtract $3$ from both sides of the equation.

$5 t - 4 w t = 8 w - 3$

Step 4

Factor $t$ out of $5 t - 4 w t$ .

Factor $t$ out of $5 t$ .

$t \cdot 5 - 4 w t = 8 w - 3$

Factor $t$ out of $- 4 w t$ .

$t \cdot 5 + t (- 4 w) = 8 w - 3$

Factor $t$ out of $t \cdot 5 + t (- 4 w)$ .

$t (5 - 4 w) = 8 w - 3$

Step 5

Divide each term in $t (5 - 4 w) = 8 w - 3$ by $5 - 4 w$ and simplify.

Divide each term in $t (5 - 4 w) = 8 w - 3$ by $5 - 4 w$ .

$\frac{t (5 - 4 w)}{5 - 4 w} = \frac{8 w}{5 - 4 w} + \frac{- 3}{5 - 4 w}$

Simplify the left side.

Cancel the common factor of $5 - 4 w$ .

Cancel the common factor.

$\frac{t (5 - 4 w)}{5 - 4 w} = \frac{8 w}{5 - 4 w} + \frac{- 3}{5 - 4 w}$

Divide $t$ by $1$ .

$t = \frac{8 w}{5 - 4 w} + \frac{- 3}{5 - 4 w}$

Simplify the right side.

Combine the numerators over the common denominator.

$t = \frac{8 w - 3}{5 - 4 w}$