Find All Complex Solutions 7(y+3)=5y+8

$7 (y + 3) = 5 y + 8$

Simplify $7 (y + 3)$ .

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Rewrite.

$0 + 0 + 7 (y + 3) = 5 y + 8$

Simplify by adding zeros.

$7 (y + 3) = 5 y + 8$

Apply the distributive property.

$7 y + 7 \cdot 3 = 5 y + 8$

Multiply $7$ by $3$ .

$7 y + 21 = 5 y + 8$

Move all terms containing $y$ to the left side of the equation.

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Subtract $5 y$ from both sides of the equation.

$7 y + 21 - 5 y = 8$

Subtract $5 y$ from $7 y$ .

$2 y + 21 = 8$

Move all terms not containing $y$ to the right side of the equation.

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Subtract $21$ from both sides of the equation.

$2 y = 8 - 21$

Subtract $21$ from $8$ .

$2 y = - 13$

Divide each term in $2 y = - 13$ by $2$ and simplify.

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Divide each term in $2 y = - 13$ by $2$ .

$\frac{2 y}{2} = \frac{- 13}{2}$

Simplify the left side.

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Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 y}{2} = \frac{- 13}{2}$

Divide $y$ by $1$ .

$y = \frac{- 13}{2}$

Simplify the right side.

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Move the negative in front of the fraction.

$y = - \frac{13}{2}$