Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $2$ by $3$ .

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

Step 2.1.3

Rewrite using the commutative property of multiplication.

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

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 $x$ .

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

Step 2.1.4.1.2

Multiply $x$ by $x$ .

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

Step 2.1.4.2

Multiply $3$ by $2$ .

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

Step 2.1.5

Apply the distributive property.

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

Step 2.1.6

Rewrite using the commutative property of multiplication.

$6 x + 6 x^{2} - 1 \cdot 5 x \cdot x - x \cdot - 5 = 0$

Step 2.1.7

Multiply $- 5$ by $- 1$ .

$6 x + 6 x^{2} - 1 \cdot 5 x \cdot x + 5 x = 0$

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 $x$ .

$6 x + 6 x^{2} - 1 \cdot 5 (x \cdot x) + 5 x = 0$

Step 2.1.8.1.2

Multiply $x$ by $x$ .

$6 x + 6 x^{2} - 1 \cdot 5 x^{2} + 5 x = 0$

Step 2.1.8.2

Multiply $- 1$ by $5$ .

$6 x + 6 x^{2} - 5 x^{2} + 5 x = 0$

Step 2.2

Add $6 x$ and $5 x$ .

$6 x^{2} - 5 x^{2} + 11 x = 0$

Step 2.3

Subtract $5 x^{2}$ from $6 x^{2}$ .

$x^{2} + 11 x = 0$

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 $x^{2} + 11 x$ .

$x^{2} + 11 x = 0$

Step 5