Algebra Examples

$15 x + 6 x (2 - 3 x) = 9 x (5 - 2 x) - 36$

Step 1

Simplify $15 x + 6 x (2 - 3 x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$15 x + 6 x \cdot 2 + 6 x (- 3 x) = 9 x (5 - 2 x) - 36$

Step 1.1.2

Multiply $2$ by $6$ .

$15 x + 12 x + 6 x (- 3 x) = 9 x (5 - 2 x) - 36$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$15 x + 12 x + 6 \cdot - 3 x \cdot x = 9 x (5 - 2 x) - 36$

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 $x$ .

$15 x + 12 x + 6 \cdot - 3 (x \cdot x) = 9 x (5 - 2 x) - 36$

Step 1.1.4.1.2

Multiply $x$ by $x$ .

$15 x + 12 x + 6 \cdot - 3 x^{2} = 9 x (5 - 2 x) - 36$

Step 1.1.4.2

Multiply $6$ by $- 3$ .

$15 x + 12 x - 18 x^{2} = 9 x (5 - 2 x) - 36$

Step 1.2

Add $15 x$ and $12 x$ .

$27 x - 18 x^{2} = 9 x (5 - 2 x) - 36$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$27 x - 18 x^{2} = 9 x \cdot 5 + 9 x (- 2 x) - 36$

Step 2.2

Multiply $5$ by $9$ .

$27 x - 18 x^{2} = 45 x + 9 x (- 2 x) - 36$

Step 2.3

Rewrite using the commutative property of multiplication.

$27 x - 18 x^{2} = 45 x + 9 \cdot - 2 x \cdot x - 36$

Step 2.4

Simplify each term.

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Step 2.4.1

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

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Step 2.4.1.1

Move $x$ .

$27 x - 18 x^{2} = 45 x + 9 \cdot - 2 (x \cdot x) - 36$

Step 2.4.1.2

Multiply $x$ by $x$ .

$27 x - 18 x^{2} = 45 x + 9 \cdot - 2 x^{2} - 36$

Step 2.4.2

Multiply $9$ by $- 2$ .

$27 x - 18 x^{2} = 45 x - 18 x^{2} - 36$

Step 3

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

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Step 3.1

Subtract $45 x$ from both sides of the equation.

$27 x - 18 x^{2} - 45 x = - 18 x^{2} - 36$

Step 3.2

Add $18 x^{2}$ to both sides of the equation.

$27 x - 18 x^{2} - 45 x + 18 x^{2} = - 36$

Step 3.3

Combine the opposite terms in $27 x - 18 x^{2} - 45 x + 18 x^{2}$ .

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Step 3.3.1

Add $- 18 x^{2}$ and $18 x^{2}$ .

$27 x - 45 x + 0 = - 36$

Step 3.3.2

Add $27 x - 45 x$ and $0$ .

$27 x - 45 x = - 36$

Step 3.4

Subtract $45 x$ from $27 x$ .

$- 18 x = - 36$

Step 4

Divide each term in $- 18 x = - 36$ by $- 18$ and simplify.

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Step 4.1

Divide each term in $- 18 x = - 36$ by $- 18$ .

$\frac{- 18 x}{- 18} = \frac{- 36}{- 18}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 18$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 18 x}{- 18} = \frac{- 36}{- 18}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 36}{- 18}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 36$ by $- 18$ .

$x = 2$