Algebra Examples

$7 (- 3 c + 10) = 4 (- 6 c + 18) + 10$

Step 1

Simplify $7 (- 3 c + 10)$ .

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Step 1.1

Rewrite.

$0 + 0 + 7 (- 3 c + 10) = 4 (- 6 c + 18) + 10$

Step 1.2

Simplify by adding zeros.

$7 (- 3 c + 10) = 4 (- 6 c + 18) + 10$

Step 1.3

Apply the distributive property.

$7 (- 3 c) + 7 \cdot 10 = 4 (- 6 c + 18) + 10$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $- 3$ by $7$ .

$- 21 c + 7 \cdot 10 = 4 (- 6 c + 18) + 10$

Step 1.4.2

Multiply $7$ by $10$ .

$- 21 c + 70 = 4 (- 6 c + 18) + 10$

Step 2

Simplify $4 (- 6 c + 18) + 10$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 21 c + 70 = 4 (- 6 c) + 4 \cdot 18 + 10$

Step 2.1.2

Multiply $- 6$ by $4$ .

$- 21 c + 70 = - 24 c + 4 \cdot 18 + 10$

Step 2.1.3

Multiply $4$ by $18$ .

$- 21 c + 70 = - 24 c + 72 + 10$

Step 2.2

Add $72$ and $10$ .

$- 21 c + 70 = - 24 c + 82$

Step 3

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

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Step 3.1

Add $24 c$ to both sides of the equation.

$- 21 c + 70 + 24 c = 82$

Step 3.2

Add $- 21 c$ and $24 c$ .

$3 c + 70 = 82$

Step 4

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

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Step 4.1

Subtract $70$ from both sides of the equation.

$3 c = 82 - 70$

Step 4.2

Subtract $70$ from $82$ .

$3 c = 12$

Step 5

Divide each term in $3 c = 12$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 c = 12$ by $3$ .

$\frac{3 c}{3} = \frac{12}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 c}{3} = \frac{12}{3}$

Step 5.2.1.2

Divide $c$ by $1$ .

$c = \frac{12}{3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $12$ by $3$ .

$c = 4$