Algebra Examples

$5 (1 - 2 (2 z - 1)) = - 3 (3 z - 1) + 1$

Step 1

Simplify $5 (1 - 2 (2 z - 1))$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (1 - 2 (2 z - 1)) = - 3 (3 z - 1) + 1$

Step 1.2

Simplify by adding zeros.

$5 (1 - 2 (2 z - 1)) = - 3 (3 z - 1) + 1$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$5 (1 - 2 (2 z) - 2 \cdot - 1) = - 3 (3 z - 1) + 1$

Step 1.3.2

Multiply $2$ by $- 2$ .

$5 (1 - 4 z - 2 \cdot - 1) = - 3 (3 z - 1) + 1$

Step 1.3.3

Multiply $- 2$ by $- 1$ .

$5 (1 - 4 z + 2) = - 3 (3 z - 1) + 1$

Step 1.4

Simplify by multiplying through.

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Step 1.4.1

Add $1$ and $2$ .

$5 (- 4 z + 3) = - 3 (3 z - 1) + 1$

Step 1.4.2

Apply the distributive property.

$5 (- 4 z) + 5 \cdot 3 = - 3 (3 z - 1) + 1$

Step 1.4.3

Multiply.

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Step 1.4.3.1

Multiply $- 4$ by $5$ .

$- 20 z + 5 \cdot 3 = - 3 (3 z - 1) + 1$

Step 1.4.3.2

Multiply $5$ by $3$ .

$- 20 z + 15 = - 3 (3 z - 1) + 1$

Step 2

Simplify $- 3 (3 z - 1) + 1$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 20 z + 15 = - 3 (3 z) - 3 \cdot - 1 + 1$

Step 2.1.2

Multiply $3$ by $- 3$ .

$- 20 z + 15 = - 9 z - 3 \cdot - 1 + 1$

Step 2.1.3

Multiply $- 3$ by $- 1$ .

$- 20 z + 15 = - 9 z + 3 + 1$

Step 2.2

Add $3$ and $1$ .

$- 20 z + 15 = - 9 z + 4$

Step 3

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

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Step 3.1

Add $9 z$ to both sides of the equation.

$- 20 z + 15 + 9 z = 4$

Step 3.2

Add $- 20 z$ and $9 z$ .

$- 11 z + 15 = 4$

Step 4

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

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Step 4.1

Subtract $15$ from both sides of the equation.

$- 11 z = 4 - 15$

Step 4.2

Subtract $15$ from $4$ .

$- 11 z = - 11$

Step 5

Divide each term in $- 11 z = - 11$ by $- 11$ and simplify.

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Step 5.1

Divide each term in $- 11 z = - 11$ by $- 11$ .

$\frac{- 11 z}{- 11} = \frac{- 11}{- 11}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 11$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 11 z}{- 11} = \frac{- 11}{- 11}$

Step 5.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 11}{- 11}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 11$ by $- 11$ .

$z = 1$