Solve for z 88z+17z+65-28-69z=-2z+44-48z-67-61z

$88 z + 17 z + 65 - 28 - 69 z = - 2 z + 44 - 48 z - 67 - 61 z$

Step 1

Simplify $88 z + 17 z + 65 - 28 - 69 z$ .

Add $88 z$ and $17 z$ .

$105 z + 65 - 28 - 69 z = - 2 z + 44 - 48 z - 67 - 61 z$

Subtract $69 z$ from $105 z$ .

$36 z + 65 - 28 = - 2 z + 44 - 48 z - 67 - 61 z$

Subtract $28$ from $65$ .

$36 z + 37 = - 2 z + 44 - 48 z - 67 - 61 z$

Step 2

Simplify $- 2 z + 44 - 48 z - 67 - 61 z$ .

Subtract $48 z$ from $- 2 z$ .

$36 z + 37 = - 50 z + 44 - 67 - 61 z$

Subtract $61 z$ from $- 50 z$ .

$36 z + 37 = - 111 z + 44 - 67$

Subtract $67$ from $44$ .

$36 z + 37 = - 111 z - 23$

Step 3

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

Add $111 z$ to both sides of the equation.

$36 z + 37 + 111 z = - 23$

Add $36 z$ and $111 z$ .

$147 z + 37 = - 23$

Step 4

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

Subtract $37$ from both sides of the equation.

$147 z = - 23 - 37$

Subtract $37$ from $- 23$ .

$147 z = - 60$

Step 5

Divide each term in $147 z = - 60$ by $147$ and simplify.

Divide each term in $147 z = - 60$ by $147$ .

$\frac{147 z}{147} = \frac{- 60}{147}$

Simplify the left side.

Cancel the common factor of $147$ .

Cancel the common factor.

$\frac{147 z}{147} = \frac{- 60}{147}$

Divide $z$ by $1$ .

$z = \frac{- 60}{147}$

Simplify the right side.

Cancel the common factor of $- 60$ and $147$ .

Factor $3$ out of $- 60$ .

$z = \frac{3 (- 20)}{147}$

Cancel the common factors.

Factor $3$ out of $147$ .

$z = \frac{3 \cdot - 20}{3 \cdot 49}$

Cancel the common factor.

$z = \frac{3 \cdot - 20}{3 \cdot 49}$

Rewrite the expression.

$z = \frac{- 20}{49}$

Move the negative in front of the fraction.

$z = - \frac{20}{49}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{20}{49}$

Decimal Form:

$z = - 0.40816326 \dots$

Solve for z 88z+17z+65-28-69z=-2z+44-48z-67-61z

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