Algebra Examples

$2 (x^{2} - 4 x) - 5 = 2 x^{2} - 6 x + 9$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 x^{2} + 2 (- 4 x) - 5 = 2 x^{2} - 6 x + 9$

Step 1.2

Multiply $- 4$ by $2$ .

$2 x^{2} - 8 x - 5 = 2 x^{2} - 6 x + 9$

Step 2

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

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Step 2.1

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

$2 x^{2} - 8 x - 5 - 2 x^{2} = - 6 x + 9$

Step 2.2

Add $6 x$ to both sides of the equation.

$2 x^{2} - 8 x - 5 - 2 x^{2} + 6 x = 9$

Step 2.3

Combine the opposite terms in $2 x^{2} - 8 x - 5 - 2 x^{2} + 6 x$ .

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Step 2.3.1

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

$- 8 x - 5 + 0 + 6 x = 9$

Step 2.3.2

Add $- 8 x - 5$ and $0$ .

$- 8 x - 5 + 6 x = 9$

Step 2.4

Add $- 8 x$ and $6 x$ .

$- 2 x - 5 = 9$

Step 3

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

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Step 3.1

Add $5$ to both sides of the equation.

$- 2 x = 9 + 5$

Step 3.2

Add $9$ and $5$ .

$- 2 x = 14$

Step 4

Divide each term in $- 2 x = 14$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x = 14$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{14}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{14}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $14$ by $- 2$ .

$x = - 7$