Solve for y 15(y-4)-2(y-9)+5(y+6)=0

$15 (y - 4) - 2 (y - 9) + 5 (y + 6) = 0$

Simplify $15 (y - 4) - 2 (y - 9) + 5 (y + 6)$ .

Simplify each term.

Apply the distributive property.

$15 y + 15 \cdot - 4 - 2 (y - 9) + 5 (y + 6) = 0$

Multiply $15$ by $- 4$ .

$15 y - 60 - 2 (y - 9) + 5 (y + 6) = 0$

Apply the distributive property.

$15 y - 60 - 2 y - 2 \cdot - 9 + 5 (y + 6) = 0$

Multiply $- 2$ by $- 9$ .

$15 y - 60 - 2 y + 18 + 5 (y + 6) = 0$

Apply the distributive property.

$15 y - 60 - 2 y + 18 + 5 y + 5 \cdot 6 = 0$

Multiply $5$ by $6$ .

$15 y - 60 - 2 y + 18 + 5 y + 30 = 0$

$15 y - 60 - 2 y + 18 + 5 y + 30 = 0$

Simplify by adding terms.

Subtract $2 y$ from $15 y$ .

$13 y - 60 + 18 + 5 y + 30 = 0$

Add $13 y$ and $5 y$ .

$18 y - 60 + 18 + 30 = 0$

Simplify by adding numbers.

Add $- 60$ and $18$ .

$18 y - 42 + 30 = 0$

Add $- 42$ and $30$ .

$18 y - 12 = 0$

$18 y - 12 = 0$

$18 y - 12 = 0$

$18 y - 12 = 0$

Add $12$ to both sides of the equation.

$18 y = 12$

Divide each term in $18 y = 12$ by $18$ and simplify.

Divide each term in $18 y = 12$ by $18$ .

$\frac{18 y}{18} = \frac{12}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 y}{18} = \frac{12}{18}$

Divide $y$ by $1$ .

$y = \frac{12}{18}$

$y = \frac{12}{18}$

$y = \frac{12}{18}$

Simplify the right side.

Cancel the common factor of $12$ and $18$ .

Factor $6$ out of $12$ .

$y = \frac{6 (2)}{18}$

Cancel the common factors.

Factor $6$ out of $18$ .

$y = \frac{6 \cdot 2}{6 \cdot 3}$

Cancel the common factor.

$y = \frac{6 \cdot 2}{6 \cdot 3}$

Rewrite the expression.

$y = \frac{2}{3}$

$y = \frac{2}{3}$

$y = \frac{2}{3}$

$y = \frac{2}{3}$

$y = \frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{2}{3}$

Decimal Form:

$y = 0.\overline{6}$

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