Algebra Examples

$(3 + 5 x) (2 - 3 x) = 12 - 15 x^{2}$

Step 1

Simplify $(3 + 5 x) (2 - 3 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + (3 + 5 x) (2 - 3 x) = 12 - 15 x^{2}$

Step 1.2

Simplify by adding zeros.

$(3 + 5 x) (2 - 3 x) = 12 - 15 x^{2}$

Step 1.3

Expand $(3 + 5 x) (2 - 3 x)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$3 (2 - 3 x) + 5 x (2 - 3 x) = 12 - 15 x^{2}$

Step 1.3.2

Apply the distributive property.

$3 \cdot 2 + 3 (- 3 x) + 5 x (2 - 3 x) = 12 - 15 x^{2}$

Step 1.3.3

Apply the distributive property.

$3 \cdot 2 + 3 (- 3 x) + 5 x \cdot 2 + 5 x (- 3 x) = 12 - 15 x^{2}$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $3$ by $2$ .

$6 + 3 (- 3 x) + 5 x \cdot 2 + 5 x (- 3 x) = 12 - 15 x^{2}$

Step 1.4.1.2

Multiply $- 3$ by $3$ .

$6 - 9 x + 5 x \cdot 2 + 5 x (- 3 x) = 12 - 15 x^{2}$

Step 1.4.1.3

Multiply $2$ by $5$ .

$6 - 9 x + 10 x + 5 x (- 3 x) = 12 - 15 x^{2}$

Step 1.4.1.4

Rewrite using the commutative property of multiplication.

$6 - 9 x + 10 x + 5 \cdot - 3 x \cdot x = 12 - 15 x^{2}$

Step 1.4.1.5

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

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Step 1.4.1.5.1

Move $x$ .

$6 - 9 x + 10 x + 5 \cdot - 3 (x \cdot x) = 12 - 15 x^{2}$

Step 1.4.1.5.2

Multiply $x$ by $x$ .

$6 - 9 x + 10 x + 5 \cdot - 3 x^{2} = 12 - 15 x^{2}$

Step 1.4.1.6

Multiply $5$ by $- 3$ .

$6 - 9 x + 10 x - 15 x^{2} = 12 - 15 x^{2}$

Step 1.4.2

Add $- 9 x$ and $10 x$ .

$6 + x - 15 x^{2} = 12 - 15 x^{2}$

Step 2

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

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Step 2.1

Add $15 x^{2}$ to both sides of the equation.

$6 + x - 15 x^{2} + 15 x^{2} = 12$

Step 2.2

Combine the opposite terms in $6 + x - 15 x^{2} + 15 x^{2}$ .

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Step 2.2.1

Add $- 15 x^{2}$ and $15 x^{2}$ .

$6 + x + 0 = 12$

Step 2.2.2

Add $6 + x$ and $0$ .

$6 + x = 12$

Step 3

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

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Step 3.1

Subtract $6$ from both sides of the equation.

$x = 12 - 6$

Step 3.2

Subtract $6$ from $12$ .

$x = 6$