Solve for r 4(2r-17)+5(3r-8)=0

$4 (2 r - 17) + 5 (3 r - 8) = 0$

Simplify $4 (2 r - 17) + 5 (3 r - 8)$ .

Simplify each term.

Apply the distributive property.

$4 (2 r) + 4 \cdot - 17 + 5 (3 r - 8) = 0$

Multiply $2$ by $4$ .

$8 r + 4 \cdot - 17 + 5 (3 r - 8) = 0$

Multiply $4$ by $- 17$ .

$8 r - 68 + 5 (3 r - 8) = 0$

Apply the distributive property.

$8 r - 68 + 5 (3 r) + 5 \cdot - 8 = 0$

Multiply $3$ by $5$ .

$8 r - 68 + 15 r + 5 \cdot - 8 = 0$

Multiply $5$ by $- 8$ .

$8 r - 68 + 15 r - 40 = 0$

$8 r - 68 + 15 r - 40 = 0$

Simplify by adding terms.

Add $8 r$ and $15 r$ .

$23 r - 68 - 40 = 0$

Subtract $40$ from $- 68$ .

$23 r - 108 = 0$

$23 r - 108 = 0$

$23 r - 108 = 0$

Add $108$ to both sides of the equation.

$23 r = 108$

Divide each term in $23 r = 108$ by $23$ and simplify.

Divide each term in $23 r = 108$ by $23$ .

$\frac{23 r}{23} = \frac{108}{23}$

Simplify the left side.

Cancel the common factor of $23$ .

Cancel the common factor.

$\frac{23 r}{23} = \frac{108}{23}$

Divide $r$ by $1$ .

$r = \frac{108}{23}$

$r = \frac{108}{23}$

$r = \frac{108}{23}$

$r = \frac{108}{23}$

The result can be shown in multiple forms.

Exact Form:

$r = \frac{108}{23}$

Decimal Form:

$r = 4.69565217 \dots$

Mixed Number Form:

$r = 4 \frac{16}{23}$

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