Algebra Examples

$5 x (3 x + 4) - 6 x (2 x - 7) = 3 x (x + 10) + 4 (4 x + 8)$

Step 1

Simplify $5 x (3 x + 4) - 6 x (2 x - 7)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 x (3 x) + 5 x \cdot 4 - 6 x (2 x - 7) = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$5 \cdot 3 x \cdot x + 5 x \cdot 4 - 6 x (2 x - 7) = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.3

Multiply $4$ by $5$ .

$5 \cdot 3 x \cdot x + 20 x - 6 x (2 x - 7) = 3 x (x + 10) + 4 (4 x + 8)$

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 $x$ .

$5 \cdot 3 (x \cdot x) + 20 x - 6 x (2 x - 7) = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.4.1.2

Multiply $x$ by $x$ .

$5 \cdot 3 x^{2} + 20 x - 6 x (2 x - 7) = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.4.2

Multiply $5$ by $3$ .

$15 x^{2} + 20 x - 6 x (2 x - 7) = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.5

Apply the distributive property.

$15 x^{2} + 20 x - 6 x (2 x) - 6 x \cdot - 7 = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.6

Rewrite using the commutative property of multiplication.

$15 x^{2} + 20 x - 6 \cdot 2 x \cdot x - 6 x \cdot - 7 = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.7

Multiply $- 7$ by $- 6$ .

$15 x^{2} + 20 x - 6 \cdot 2 x \cdot x + 42 x = 3 x (x + 10) + 4 (4 x + 8)$

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 $x$ .

$15 x^{2} + 20 x - 6 \cdot 2 (x \cdot x) + 42 x = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.8.1.2

Multiply $x$ by $x$ .

$15 x^{2} + 20 x - 6 \cdot 2 x^{2} + 42 x = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.1.8.2

Multiply $- 6$ by $2$ .

$15 x^{2} + 20 x - 12 x^{2} + 42 x = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $12 x^{2}$ from $15 x^{2}$ .

$3 x^{2} + 20 x + 42 x = 3 x (x + 10) + 4 (4 x + 8)$

Step 1.2.2

Add $20 x$ and $42 x$ .

$3 x^{2} + 62 x = 3 x (x + 10) + 4 (4 x + 8)$

Step 2

Simplify $3 x (x + 10) + 4 (4 x + 8)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 x^{2} + 62 x = 3 x \cdot x + 3 x \cdot 10 + 4 (4 x + 8)$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$3 x^{2} + 62 x = 3 (x \cdot x) + 3 x \cdot 10 + 4 (4 x + 8)$

Step 2.1.2.2

Multiply $x$ by $x$ .

$3 x^{2} + 62 x = 3 x^{2} + 3 x \cdot 10 + 4 (4 x + 8)$

Step 2.1.3

Multiply $10$ by $3$ .

$3 x^{2} + 62 x = 3 x^{2} + 30 x + 4 (4 x + 8)$

Step 2.1.4

Apply the distributive property.

$3 x^{2} + 62 x = 3 x^{2} + 30 x + 4 (4 x) + 4 \cdot 8$

Step 2.1.5

Multiply $4$ by $4$ .

$3 x^{2} + 62 x = 3 x^{2} + 30 x + 16 x + 4 \cdot 8$

Step 2.1.6

Multiply $4$ by $8$ .

$3 x^{2} + 62 x = 3 x^{2} + 30 x + 16 x + 32$

Step 2.2

Add $30 x$ and $16 x$ .

$3 x^{2} + 62 x = 3 x^{2} + 46 x + 32$

Step 3

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

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Step 3.1

Subtract $3 x^{2}$ from both sides of the equation.

$3 x^{2} + 62 x - 3 x^{2} = 46 x + 32$

Step 3.2

Subtract $46 x$ from both sides of the equation.

$3 x^{2} + 62 x - 3 x^{2} - 46 x = 32$

Step 3.3

Combine the opposite terms in $3 x^{2} + 62 x - 3 x^{2} - 46 x$ .

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Step 3.3.1

Subtract $3 x^{2}$ from $3 x^{2}$ .

$62 x + 0 - 46 x = 32$

Step 3.3.2

Add $62 x$ and $0$ .

$62 x - 46 x = 32$

Step 3.4

Subtract $46 x$ from $62 x$ .

$16 x = 32$

Step 4

Divide each term in $16 x = 32$ by $16$ and simplify.

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Step 4.1

Divide each term in $16 x = 32$ by $16$ .

$\frac{16 x}{16} = \frac{32}{16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{32}{16}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{32}{16}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $32$ by $16$ .

$x = 2$