Algebra Examples

$2 x (9 - 5 x) = - 5 x (2 - 3 x)$

Step 1

Add $5 x (2 - 3 x)$ to both sides of the equation.

$2 x (9 - 5 x) + 5 x (2 - 3 x) = 0$

Step 2

Simplify $2 x (9 - 5 x) + 5 x (2 - 3 x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 x \cdot 9 + 2 x (- 5 x) + 5 x (2 - 3 x) = 0$

Step 2.1.2

Multiply $9$ by $2$ .

$18 x + 2 x (- 5 x) + 5 x (2 - 3 x) = 0$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$18 x + 2 \cdot - 5 x \cdot x + 5 x (2 - 3 x) = 0$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

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

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Step 2.1.4.1.1

Move $x$ .

$18 x + 2 \cdot - 5 (x \cdot x) + 5 x (2 - 3 x) = 0$

Step 2.1.4.1.2

Multiply $x$ by $x$ .

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

Step 2.1.4.2

Multiply $2$ by $- 5$ .

$18 x - 10 x^{2} + 5 x (2 - 3 x) = 0$

Step 2.1.5

Apply the distributive property.

$18 x - 10 x^{2} + 5 x \cdot 2 + 5 x (- 3 x) = 0$

Step 2.1.6

Multiply $2$ by $5$ .

$18 x - 10 x^{2} + 10 x + 5 x (- 3 x) = 0$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$18 x - 10 x^{2} + 10 x + 5 \cdot - 3 x \cdot x = 0$

Step 2.1.8

Simplify each term.

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Step 2.1.8.1

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

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Step 2.1.8.1.1

Move $x$ .

$18 x - 10 x^{2} + 10 x + 5 \cdot - 3 (x \cdot x) = 0$

Step 2.1.8.1.2

Multiply $x$ by $x$ .

$18 x - 10 x^{2} + 10 x + 5 \cdot - 3 x^{2} = 0$

Step 2.1.8.2

Multiply $5$ by $- 3$ .

$18 x - 10 x^{2} + 10 x - 15 x^{2} = 0$

Step 2.2

Add $18 x$ and $10 x$ .

$- 10 x^{2} + 28 x - 15 x^{2} = 0$

Step 2.3

Subtract $15 x^{2}$ from $- 10 x^{2}$ .

$- 25 x^{2} + 28 x = 0$

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 $- 25 x^{2} + 28 x$ .

$- 25 x^{2} + 28 x = 0$

Step 5