Algebra Examples

$- 9 x (4 x - 1) - 2 x (- 18 x - 6) - 60 = 3$

Step 1

Simplify $- 9 x (4 x - 1) - 2 x (- 18 x - 6) - 60$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 9 x (4 x) - 9 x \cdot - 1 - 2 x (- 18 x - 6) - 60 = 3$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$- 9 \cdot 4 x \cdot x - 9 x \cdot - 1 - 2 x (- 18 x - 6) - 60 = 3$

Step 1.1.3

Multiply $- 1$ by $- 9$ .

$- 9 \cdot 4 x \cdot x + 9 x - 2 x (- 18 x - 6) - 60 = 3$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

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

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Step 1.1.4.1.1

Move $x$ .

$- 9 \cdot 4 (x \cdot x) + 9 x - 2 x (- 18 x - 6) - 60 = 3$

Step 1.1.4.1.2

Multiply $x$ by $x$ .

$- 9 \cdot 4 x^{2} + 9 x - 2 x (- 18 x - 6) - 60 = 3$

Step 1.1.4.2

Multiply $- 9$ by $4$ .

$- 36 x^{2} + 9 x - 2 x (- 18 x - 6) - 60 = 3$

Step 1.1.5

Apply the distributive property.

$- 36 x^{2} + 9 x - 2 x (- 18 x) - 2 x \cdot - 6 - 60 = 3$

Step 1.1.6

Rewrite using the commutative property of multiplication.

$- 36 x^{2} + 9 x - 2 \cdot - 18 x \cdot x - 2 x \cdot - 6 - 60 = 3$

Step 1.1.7

Multiply $- 6$ by $- 2$ .

$- 36 x^{2} + 9 x - 2 \cdot - 18 x \cdot x + 12 x - 60 = 3$

Step 1.1.8

Simplify each term.

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Step 1.1.8.1

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

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Step 1.1.8.1.1

Move $x$ .

$- 36 x^{2} + 9 x - 2 \cdot - 18 (x \cdot x) + 12 x - 60 = 3$

Step 1.1.8.1.2

Multiply $x$ by $x$ .

$- 36 x^{2} + 9 x - 2 \cdot - 18 x^{2} + 12 x - 60 = 3$

Step 1.1.8.2

Multiply $- 2$ by $- 18$ .

$- 36 x^{2} + 9 x + 36 x^{2} + 12 x - 60 = 3$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $- 36 x^{2} + 9 x + 36 x^{2} + 12 x - 60$ .

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Step 1.2.1.1

Add $- 36 x^{2}$ and $36 x^{2}$ .

$9 x + 0 + 12 x - 60 = 3$

Step 1.2.1.2

Add $9 x$ and $0$ .

$9 x + 12 x - 60 = 3$

Step 1.2.2

Add $9 x$ and $12 x$ .

$21 x - 60 = 3$

Step 2

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

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Step 2.1

Add $60$ to both sides of the equation.

$21 x = 3 + 60$

Step 2.2

Add $3$ and $60$ .

$21 x = 63$

Step 3

Divide each term in $21 x = 63$ by $21$ and simplify.

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Step 3.1

Divide each term in $21 x = 63$ by $21$ .

$\frac{21 x}{21} = \frac{63}{21}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $21$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{21 x}{21} = \frac{63}{21}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{63}{21}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $63$ by $21$ .

$x = 3$