Algebra Examples

$2 x (x - 5) = 6 x^{2} - 11 x$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $6 x^{2}$ from both sides of the equation.

$2 x (x - 5) - 6 x^{2} = - 11 x$

Step 1.2

Add $11 x$ to both sides of the equation.

$2 x (x - 5) - 6 x^{2} + 11 x = 0$

Step 2

Simplify $2 x (x - 5) - 6 x^{2} + 11 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 5 - 6 x^{2} + 11 x = 0$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 5 - 6 x^{2} + 11 x = 0$

Step 2.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 5 - 6 x^{2} + 11 x = 0$

Step 2.1.3

Multiply $- 5$ by $2$ .

$2 x^{2} - 10 x - 6 x^{2} + 11 x = 0$

Step 2.2

Subtract $6 x^{2}$ from $2 x^{2}$ .

$- 4 x^{2} - 10 x + 11 x = 0$

Step 2.3

Add $- 10 x$ and $11 x$ .

$- 4 x^{2} + x = 0$

Step 3

Factor $x$ out of $- 4 x^{2} + x$ .

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Step 3.1

Factor $x$ out of $- 4 x^{2}$ .

$x (- 4 x) + x = 0$

Step 3.2

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

$x (- 4 x) + x = 0$

Step 3.3

Factor $x$ out of $x^{1}$ .

$x (- 4 x) + x \cdot 1 = 0$

Step 3.4

Factor $x$ out of $x (- 4 x) + x \cdot 1$ .

$x (- 4 x + 1) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$- 4 x + 1 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $- 4 x + 1$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $- 4 x + 1$ equal to $0$ .

$- 4 x + 1 = 0$

Step 6.2

Solve $- 4 x + 1 = 0$ for $x$ .

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Step 6.2.1

Subtract $1$ from both sides of the equation.

$- 4 x = - 1$

Step 6.2.2

Divide each term in $- 4 x = - 1$ by $- 4$ and simplify.

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Step 6.2.2.1

Divide each term in $- 4 x = - 1$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 1}{- 4}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $- 4$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 1}{- 4}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 4}$

Step 6.2.2.3

Simplify the right side.

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Step 6.2.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{4}$

Step 7

The final solution is all the values that make $x (- 4 x + 1) = 0$ true.

$x = 0, \frac{1}{4}$