Algebra Examples

$- 3 (3 c + 5) = 2 (10 - c)$

Step 1

Simplify $- 3 (3 c + 5)$ .

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Step 1.1

Rewrite.

$0 + 0 - 3 (3 c + 5) = 2 (10 - c)$

Step 1.2

Simplify by adding zeros.

$- 3 (3 c + 5) = 2 (10 - c)$

Step 1.3

Apply the distributive property.

$- 3 (3 c) - 3 \cdot 5 = 2 (10 - c)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $- 3$ .

$- 9 c - 3 \cdot 5 = 2 (10 - c)$

Step 1.4.2

Multiply $- 3$ by $5$ .

$- 9 c - 15 = 2 (10 - c)$

Step 2

Simplify $2 (10 - c)$ .

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Step 2.1

Apply the distributive property.

$- 9 c - 15 = 2 \cdot 10 + 2 (- c)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $10$ .

$- 9 c - 15 = 20 + 2 (- c)$

Step 2.2.2

Multiply $- 1$ by $2$ .

$- 9 c - 15 = 20 - 2 c$

Step 3

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

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Step 3.1

Add $2 c$ to both sides of the equation.

$- 9 c - 15 + 2 c = 20$

Step 3.2

Add $- 9 c$ and $2 c$ .

$- 7 c - 15 = 20$

Step 4

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

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Step 4.1

Add $15$ to both sides of the equation.

$- 7 c = 20 + 15$

Step 4.2

Add $20$ and $15$ .

$- 7 c = 35$

Step 5

Divide each term in $- 7 c = 35$ by $- 7$ and simplify.

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Step 5.1

Divide each term in $- 7 c = 35$ by $- 7$ .

$\frac{- 7 c}{- 7} = \frac{35}{- 7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 7 c}{- 7} = \frac{35}{- 7}$

Step 5.2.1.2

Divide $c$ by $1$ .

$c = \frac{35}{- 7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $35$ by $- 7$ .

$c = - 5$