Algebra Examples

$(x - 6) (x + 3) = x (2 x - 5)$

Step 1

Subtract $x (2 x - 5)$ from both sides of the equation.

$(x - 6) (x + 3) - x (2 x - 5) = 0$

Step 2

Simplify $(x - 6) (x + 3) - x (2 x - 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(x - 6) (x + 3)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$x (x + 3) - 6 (x + 3) - x (2 x - 5) = 0$

Step 2.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 3 - 6 (x + 3) - x (2 x - 5) = 0$

Step 2.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 3 - 6 x - 6 \cdot 3 - x (2 x - 5) = 0$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 - 6 x - 6 \cdot 3 - x (2 x - 5) = 0$

Step 2.1.2.1.2

Move $3$ to the left of $x$ .

$x^{2} + 3 \cdot x - 6 x - 6 \cdot 3 - x (2 x - 5) = 0$

Step 2.1.2.1.3

Multiply $- 6$ by $3$ .

$x^{2} + 3 x - 6 x - 18 - x (2 x - 5) = 0$

Step 2.1.2.2

Subtract $6 x$ from $3 x$ .

$x^{2} - 3 x - 18 - x (2 x - 5) = 0$

Step 2.1.3

Apply the distributive property.

$x^{2} - 3 x - 18 - x (2 x) - x \cdot - 5 = 0$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$x^{2} - 3 x - 18 - 1 \cdot 2 x \cdot x - x \cdot - 5 = 0$

Step 2.1.5

Multiply $- 5$ by $- 1$ .

$x^{2} - 3 x - 18 - 1 \cdot 2 x \cdot x + 5 x = 0$

Step 2.1.6

Simplify each term.

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Step 2.1.6.1

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

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Step 2.1.6.1.1

Move $x$ .

$x^{2} - 3 x - 18 - 1 \cdot 2 (x \cdot x) + 5 x = 0$

Step 2.1.6.1.2

Multiply $x$ by $x$ .

$x^{2} - 3 x - 18 - 1 \cdot 2 x^{2} + 5 x = 0$

Step 2.1.6.2

Multiply $- 1$ by $2$ .

$x^{2} - 3 x - 18 - 2 x^{2} + 5 x = 0$

Step 2.2

Subtract $2 x^{2}$ from $x^{2}$ .

$- x^{2} - 3 x - 18 + 5 x = 0$

Step 2.3

Add $- 3 x$ and $5 x$ .

$- x^{2} + 2 x - 18 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $- x^{2} + 2 x - 18$ .

$- x^{2} + 2 x - 18 = 0$

Step 5