Basic Math Examples

$45 - (2 c + 4) = 4 (c + 5) + c$

Step 1

Since $c$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 (c + 5) + c = 45 - (2 c + 4)$

Step 2

Simplify $4 (c + 5) + c$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 c + 4 \cdot 5 + c = 45 - (2 c + 4)$

Step 2.1.2

Multiply $4$ by $5$ .

$4 c + 20 + c = 45 - (2 c + 4)$

Step 2.2

Add $4 c$ and $c$ .

$5 c + 20 = 45 - (2 c + 4)$

Step 3

Simplify $45 - (2 c + 4)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$5 c + 20 = 45 - (2 c) - 1 \cdot 4$

Step 3.1.2

Multiply $2$ by $- 1$ .

$5 c + 20 = 45 - 2 c - 1 \cdot 4$

Step 3.1.3

Multiply $- 1$ by $4$ .

$5 c + 20 = 45 - 2 c - 4$

Step 3.2

Subtract $4$ from $45$ .

$5 c + 20 = - 2 c + 41$

Step 4

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

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Step 4.1

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

$5 c + 20 + 2 c = 41$

Step 4.2

Add $5 c$ and $2 c$ .

$7 c + 20 = 41$

Step 5

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

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Step 5.1

Subtract $20$ from both sides of the equation.

$7 c = 41 - 20$

Step 5.2

Subtract $20$ from $41$ .

$7 c = 21$

Step 6

Divide each term in $7 c = 21$ by $7$ and simplify.

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Step 6.1

Divide each term in $7 c = 21$ by $7$ .

$\frac{7 c}{7} = \frac{21}{7}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $7$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{7 c}{7} = \frac{21}{7}$

Step 6.2.1.2

Divide $c$ by $1$ .

$c = \frac{21}{7}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $21$ by $7$ .

$c = 3$