Algebra Examples

$x (2 x - 1) = 2 x^{2} + 5 x - 12$

Step 1

Simplify $x (2 x - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + x (2 x - 1) = 2 x^{2} + 5 x - 12$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$x (2 x) + x \cdot - 1 = 2 x^{2} + 5 x - 12$

Step 1.2.2

Reorder.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 1 = 2 x^{2} + 5 x - 12$

Step 1.2.2.2

Move $- 1$ to the left of $x$ .

$2 x \cdot x - 1 \cdot x = 2 x^{2} + 5 x - 12$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $x$ .

$2 (x \cdot x) - 1 \cdot x = 2 x^{2} + 5 x - 12$

Step 1.3.1.2

Multiply $x$ by $x$ .

$2 x^{2} - 1 \cdot x = 2 x^{2} + 5 x - 12$

Step 1.3.2

Rewrite $- 1 x$ as $- x$ .

$2 x^{2} - x = 2 x^{2} + 5 x - 12$

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.

$2 x^{2} - x - 2 x^{2} = 5 x - 12$

Step 2.2

Subtract $5 x$ from both sides of the equation.

$2 x^{2} - x - 2 x^{2} - 5 x = - 12$

Step 2.3

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

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Step 2.3.1

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

$- x + 0 - 5 x = - 12$

Step 2.3.2

Add $- x$ and $0$ .

$- x - 5 x = - 12$

Step 2.4

Subtract $5 x$ from $- x$ .

$- 6 x = - 12$

Step 3

Divide each term in $- 6 x = - 12$ by $- 6$ and simplify.

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Step 3.1

Divide each term in $- 6 x = - 12$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 12}{- 6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{- 6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 12$ by $- 6$ .

$x = 2$