Algebra Examples

$5 x^{2} (3 x + 6) = 3 (5 x^{3} + 10 x^{2} + x - 9)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 (5 x^{3} + 10 x^{2} + x - 9) = 5 x^{2} (3 x + 6)$

Step 2

Simplify $3 (5 x^{3} + 10 x^{2} + x - 9)$ .

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Step 2.1

Rewrite.

$0 + 0 + 3 (5 x^{3} + 10 x^{2} + x - 9) = 5 x^{2} (3 x + 6)$

Step 2.2

Simplify by adding zeros.

$3 (5 x^{3} + 10 x^{2} + x - 9) = 5 x^{2} (3 x + 6)$

Step 2.3

Apply the distributive property.

$3 (5 x^{3}) + 3 (10 x^{2}) + 3 x + 3 \cdot - 9 = 5 x^{2} (3 x + 6)$

Step 2.4

Simplify.

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Step 2.4.1

Multiply $5$ by $3$ .

$15 x^{3} + 3 (10 x^{2}) + 3 x + 3 \cdot - 9 = 5 x^{2} (3 x + 6)$

Step 2.4.2

Multiply $10$ by $3$ .

$15 x^{3} + 30 x^{2} + 3 x + 3 \cdot - 9 = 5 x^{2} (3 x + 6)$

Step 2.4.3

Multiply $3$ by $- 9$ .

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 x^{2} (3 x + 6)$

Step 3

Simplify $5 x^{2} (3 x + 6)$ .

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Step 3.1

Simplify by multiplying through.

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Step 3.1.1

Apply the distributive property.

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 x^{2} (3 x) + 5 x^{2} \cdot 6$

Step 3.1.2

Simplify the expression.

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Step 3.1.2.1

Rewrite using the commutative property of multiplication.

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 \cdot 3 x^{2} x + 5 x^{2} \cdot 6$

Step 3.1.2.2

Multiply $6$ by $5$ .

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 \cdot 3 x^{2} x + 30 x^{2}$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 3.2.1.1

Move $x$ .

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 \cdot 3 (x \cdot x^{2}) + 30 x^{2}$

Step 3.2.1.2

Multiply $x$ by $x^{2}$ .

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Step 3.2.1.2.1

Raise $x$ to the power of $1$ .

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 \cdot 3 (x^{1} x^{2}) + 30 x^{2}$

Step 3.2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 \cdot 3 x^{1 + 2} + 30 x^{2}$

Step 3.2.1.3

Add $1$ and $2$ .

$15 x^{3} + 30 x^{2} + 3 x - 27 = 5 \cdot 3 x^{3} + 30 x^{2}$

Step 3.2.2

Multiply $5$ by $3$ .

$15 x^{3} + 30 x^{2} + 3 x - 27 = 15 x^{3} + 30 x^{2}$

Step 4

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

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Step 4.1

Subtract $15 x^{3}$ from both sides of the equation.

$15 x^{3} + 30 x^{2} + 3 x - 27 - 15 x^{3} = 30 x^{2}$

Step 4.2

Subtract $30 x^{2}$ from both sides of the equation.

$15 x^{3} + 30 x^{2} + 3 x - 27 - 15 x^{3} - 30 x^{2} = 0$

Step 4.3

Combine the opposite terms in $15 x^{3} + 30 x^{2} + 3 x - 27 - 15 x^{3} - 30 x^{2}$ .

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Step 4.3.1

Subtract $15 x^{3}$ from $15 x^{3}$ .

$30 x^{2} + 3 x - 27 + 0 - 30 x^{2} = 0$

Step 4.3.2

Add $30 x^{2} + 3 x - 27$ and $0$ .

$30 x^{2} + 3 x - 27 - 30 x^{2} = 0$

Step 4.3.3

Subtract $30 x^{2}$ from $30 x^{2}$ .

$3 x - 27 + 0 = 0$

Step 4.3.4

Add $3 x - 27$ and $0$ .

$3 x - 27 = 0$

Step 5

Add $27$ to both sides of the equation.

$3 x = 27$

Step 6

Divide each term in $3 x = 27$ by $3$ and simplify.

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Step 6.1

Divide each term in $3 x = 27$ by $3$ .

$\frac{3 x}{3} = \frac{27}{3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{27}{3}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{27}{3}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $27$ by $3$ .

$x = 9$