Basic Math Examples

$- 5 (1 - 5 a) + 5 (- 8 a - 2) = - 4 a - 8 a$

Step 1

Simplify $- 5 (1 - 5 a) + 5 (- 8 a - 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 5 \cdot 1 - 5 (- 5 a) + 5 (- 8 a - 2) = - 4 a - 8 a$

Step 1.1.2

Multiply $- 5$ by $1$ .

$- 5 - 5 (- 5 a) + 5 (- 8 a - 2) = - 4 a - 8 a$

Step 1.1.3

Multiply $- 5$ by $- 5$ .

$- 5 + 25 a + 5 (- 8 a - 2) = - 4 a - 8 a$

Step 1.1.4

Apply the distributive property.

$- 5 + 25 a + 5 (- 8 a) + 5 \cdot - 2 = - 4 a - 8 a$

Step 1.1.5

Multiply $- 8$ by $5$ .

$- 5 + 25 a - 40 a + 5 \cdot - 2 = - 4 a - 8 a$

Step 1.1.6

Multiply $5$ by $- 2$ .

$- 5 + 25 a - 40 a - 10 = - 4 a - 8 a$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $10$ from $- 5$ .

$25 a - 40 a - 15 = - 4 a - 8 a$

Step 1.2.2

Subtract $40 a$ from $25 a$ .

$- 15 a - 15 = - 4 a - 8 a$

Step 2

Subtract $8 a$ from $- 4 a$ .

$- 15 a - 15 = - 12 a$

Step 3

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

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Step 3.1

Add $12 a$ to both sides of the equation.

$- 15 a - 15 + 12 a = 0$

Step 3.2

Add $- 15 a$ and $12 a$ .

$- 3 a - 15 = 0$

Step 4

Add $15$ to both sides of the equation.

$- 3 a = 15$

Step 5

Divide each term in $- 3 a = 15$ by $- 3$ and simplify.

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Step 5.1

Divide each term in $- 3 a = 15$ by $- 3$ .

$\frac{- 3 a}{- 3} = \frac{15}{- 3}$

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.

$\frac{- 3 a}{- 3} = \frac{15}{- 3}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{15}{- 3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $15$ by $- 3$ .

$a = - 5$