Solve for z 2(z+13)+1=1-3(10-z)

$2 (z + 13) + 1 = 1 - 3 (10 - z)$

Simplify $2 (z + 13) + 1$ .

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Simplify each term.

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Apply the distributive property.

$2 z + 2 \cdot 13 + 1 = 1 - 3 (10 - z)$

Multiply $2$ by $13$ .

$2 z + 26 + 1 = 1 - 3 (10 - z)$

Add $26$ and $1$ .

$2 z + 27 = 1 - 3 (10 - z)$

Simplify $1 - 3 (10 - z)$ .

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Simplify each term.

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Apply the distributive property.

$2 z + 27 = 1 - 3 \cdot 10 - 3 (- z)$

Multiply $- 3$ by $10$ .

$2 z + 27 = 1 - 30 - 3 (- z)$

Multiply $- 1$ by $- 3$ .

$2 z + 27 = 1 - 30 + 3 z$

Subtract $30$ from $1$ .

$2 z + 27 = - 29 + 3 z$

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

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Subtract $3 z$ from both sides of the equation.

$2 z + 27 - 3 z = - 29$

Subtract $3 z$ from $2 z$ .

$- z + 27 = - 29$

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

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Subtract $27$ from both sides of the equation.

$- z = - 29 - 27$

Subtract $27$ from $- 29$ .

$- z = - 56$

Multiply each term in $- z = - 56$ by $- 1$

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Multiply each term in $- z = - 56$ by $- 1$ .

$(- z) \cdot - 1 = (- 56) \cdot - 1$

Multiply $(- z) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 z = (- 56) \cdot - 1$

Multiply $z$ by $1$ .

$z = (- 56) \cdot - 1$

Multiply $- 56$ by $- 1$ .

$z = 56$

Solve for z 2(z+13)+1=1-3(10-z)

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