Algebra Examples

$2 x (x + 4) + 7 = (x + 8) + 2 x (x + 1) + 12$

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.

$x + 8 + 2 x (x + 1) + 12 = 2 x (x + 4) + 7$

Step 2

Simplify $x + 8 + 2 x (x + 1) + 12$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x + 8 + 2 x \cdot x + 2 x \cdot 1 + 12 = 2 x (x + 4) + 7$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$x + 8 + 2 (x \cdot x) + 2 x \cdot 1 + 12 = 2 x (x + 4) + 7$

Step 2.1.2.2

Multiply $x$ by $x$ .

$x + 8 + 2 x^{2} + 2 x \cdot 1 + 12 = 2 x (x + 4) + 7$

Step 2.1.3

Multiply $2$ by $1$ .

$x + 8 + 2 x^{2} + 2 x + 12 = 2 x (x + 4) + 7$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $x$ and $2 x$ .

$3 x + 8 + 2 x^{2} + 12 = 2 x (x + 4) + 7$

Step 2.2.2

Add $8$ and $12$ .

$3 x + 2 x^{2} + 20 = 2 x (x + 4) + 7$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$3 x + 2 x^{2} + 20 = 2 x \cdot x + 2 x \cdot 4 + 7$

Step 3.2

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

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Step 3.2.1

Move $x$ .

$3 x + 2 x^{2} + 20 = 2 (x \cdot x) + 2 x \cdot 4 + 7$

Step 3.2.2

Multiply $x$ by $x$ .

$3 x + 2 x^{2} + 20 = 2 x^{2} + 2 x \cdot 4 + 7$

Step 3.3

Multiply $4$ by $2$ .

$3 x + 2 x^{2} + 20 = 2 x^{2} + 8 x + 7$

Step 4

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

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Step 4.1

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

$3 x + 2 x^{2} + 20 - 2 x^{2} = 8 x + 7$

Step 4.2

Subtract $8 x$ from both sides of the equation.

$3 x + 2 x^{2} + 20 - 2 x^{2} - 8 x = 7$

Step 4.3

Combine the opposite terms in $3 x + 2 x^{2} + 20 - 2 x^{2} - 8 x$ .

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Step 4.3.1

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

$3 x + 0 + 20 - 8 x = 7$

Step 4.3.2

Add $3 x$ and $0$ .

$3 x + 20 - 8 x = 7$

Step 4.4

Subtract $8 x$ from $3 x$ .

$- 5 x + 20 = 7$

Step 5

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

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Step 5.1

Subtract $20$ from both sides of the equation.

$- 5 x = 7 - 20$

Step 5.2

Subtract $20$ from $7$ .

$- 5 x = - 13$

Step 6

Divide each term in $- 5 x = - 13$ by $- 5$ and simplify.

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Step 6.1

Divide each term in $- 5 x = - 13$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 13}{- 5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 13}{- 5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 13}{- 5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Dividing two negative values results in a positive value.

$x = \frac{13}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{5}$

Decimal Form:

$x = 2.6$

Mixed Number Form:

$x = 2 \frac{3}{5}$