Precalculus Examples

$y = 2 (x - 4) (x + 3)$

Step 1

Subtract $2 (x - 4) (x + 3)$ from both sides of the equation.

$y - 2 (x - 4) (x + 3) = 0$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$y + (- 2 x - 2 \cdot - 4) (x + 3) = 0$

Step 2.2

Multiply $- 2$ by $- 4$ .

$y + (- 2 x + 8) (x + 3) = 0$

Step 2.3

Expand $(- 2 x + 8) (x + 3)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$y - 2 x (x + 3) + 8 (x + 3) = 0$

Step 2.3.2

Apply the distributive property.

$y - 2 x \cdot x - 2 x \cdot 3 + 8 (x + 3) = 0$

Step 2.3.3

Apply the distributive property.

$y - 2 x \cdot x - 2 x \cdot 3 + 8 x + 8 \cdot 3 = 0$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.4.1.1.1

Move $x$ .

$y - 2 (x \cdot x) - 2 x \cdot 3 + 8 x + 8 \cdot 3 = 0$

Step 2.4.1.1.2

Multiply $x$ by $x$ .

$y - 2 x^{2} - 2 x \cdot 3 + 8 x + 8 \cdot 3 = 0$

Step 2.4.1.2

Multiply $3$ by $- 2$ .

$y - 2 x^{2} - 6 x + 8 x + 8 \cdot 3 = 0$

Step 2.4.1.3

Multiply $8$ by $3$ .

$y - 2 x^{2} - 6 x + 8 x + 24 = 0$

Step 2.4.2

Add $- 6 x$ and $8 x$ .

$y - 2 x^{2} + 2 x + 24 = 0$

Step 3

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

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Step 3.1

Add $2 x^{2}$ to both sides of the equation.

$y + 2 x + 24 = 2 x^{2}$

Step 3.2

Subtract $2 x$ from both sides of the equation.

$y + 24 = 2 x^{2} - 2 x$

Step 3.3

Subtract $24$ from both sides of the equation.

$y = 2 x^{2} - 2 x - 24$