Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Expand $(3 z - 5) (z - 1)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

$3 z \cdot z + 3 z \cdot - 1 - 5 (z - 1) + y = 0$

Step 1.1.3

Apply the distributive property.

$3 z \cdot z + 3 z \cdot - 1 - 5 z - 5 \cdot - 1 + y = 0$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $z$ by $z$ by adding the exponents.

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Step 1.2.1.1.1

Move $z$ .

$3 (z \cdot z) + 3 z \cdot - 1 - 5 z - 5 \cdot - 1 + y = 0$

Step 1.2.1.1.2

Multiply $z$ by $z$ .

$3 z^{2} + 3 z \cdot - 1 - 5 z - 5 \cdot - 1 + y = 0$

Step 1.2.1.2

Multiply $- 1$ by $3$ .

$3 z^{2} - 3 z - 5 z - 5 \cdot - 1 + y = 0$

Step 1.2.1.3

Multiply $- 5$ by $- 1$ .

$3 z^{2} - 3 z - 5 z + 5 + y = 0$

Step 1.2.2

Subtract $5 z$ from $- 3 z$ .

$3 z^{2} - 8 z + 5 + y = 0$

Step 2

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

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Step 2.1

Subtract $3 z^{2}$ from both sides of the equation.

$- 8 z + 5 + y = - 3 z^{2}$

Step 2.2

Add $8 z$ to both sides of the equation.

$5 + y = - 3 z^{2} + 8 z$

Step 2.3

Subtract $5$ from both sides of the equation.

$y = - 3 z^{2} + 8 z - 5$