Basic Math Examples

6 (u + 8) = - 6 (2 u - 9) + 9 u

$6 (u + 8) = - 6 (2 u - 9) + 9 u$

Step 1

Since

u

$u$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

- 6 (2 u - 9) + 9 u = 6 (u + 8)

$- 6 (2 u - 9) + 9 u = 6 (u + 8)$

Step 2

Simplify

- 6 (2 u - 9) + 9 u

$- 6 (2 u - 9) + 9 u$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

- 6 (2 u) - 6 \cdot - 9 + 9 u = 6 (u + 8)

$- 6 (2 u) - 6 \cdot - 9 + 9 u = 6 (u + 8)$

Step 2.1.2

Multiply

2

$2$ by

- 6

$- 6$ .

- 12 u - 6 \cdot - 9 + 9 u = 6 (u + 8)

$- 12 u - 6 \cdot - 9 + 9 u = 6 (u + 8)$

Step 2.1.3

Multiply

- 6

$- 6$ by

- 9

$- 9$ .

- 12 u + 54 + 9 u = 6 (u + 8)

$- 12 u + 54 + 9 u = 6 (u + 8)$

- 12 u + 54 + 9 u = 6 (u + 8)

$- 12 u + 54 + 9 u = 6 (u + 8)$

Step 2.2

Add

- 12 u

$- 12 u$ and

9 u

$9 u$ .

- 3 u + 54 = 6 (u + 8)

$- 3 u + 54 = 6 (u + 8)$

- 3 u + 54 = 6 (u + 8)

$- 3 u + 54 = 6 (u + 8)$

Step 3

Simplify

6 (u + 8)

$6 (u + 8)$ .

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Step 3.1

Apply the distributive property.

- 3 u + 54 = 6 u + 6 \cdot 8

$- 3 u + 54 = 6 u + 6 \cdot 8$

Step 3.2

Multiply

6

$6$ by

8

$8$ .

- 3 u + 54 = 6 u + 48

$- 3 u + 54 = 6 u + 48$

- 3 u + 54 = 6 u + 48

$- 3 u + 54 = 6 u + 48$

Step 4

Move all terms containing

u

$u$ to the left side of the equation.

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Step 4.1

Subtract

6 u

$6 u$ from both sides of the equation.

- 3 u + 54 - 6 u = 48

$- 3 u + 54 - 6 u = 48$

Step 4.2

Subtract

6 u

$6 u$ from

- 3 u

$- 3 u$ .

- 9 u + 54 = 48

$- 9 u + 54 = 48$

- 9 u + 54 = 48

$- 9 u + 54 = 48$

Step 5

Move all terms not containing

u

$u$ to the right side of the equation.

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Step 5.1

Subtract

54

$54$ from both sides of the equation.

- 9 u = 48 - 54

$- 9 u = 48 - 54$

Step 5.2

Subtract

54

$54$ from

48

$48$ .

- 9 u = - 6

$- 9 u = - 6$

- 9 u = - 6

$- 9 u = - 6$

Step 6

Divide each term in

- 9 u = - 6

$- 9 u = - 6$ by

- 9

$- 9$ and simplify.

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Step 6.1

Divide each term in

- 9 u = - 6

$- 9 u = - 6$ by

- 9

$- 9$ .

\frac{- 9 u}{- 9} = \frac{- 6}{- 9}

$\frac{- 9 u}{- 9} = \frac{- 6}{- 9}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

- 9

$- 9$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 9 u}{- 9} = \frac{- 6}{- 9}$

Step 6.2.1.2

Divide

$u$ by

$1$ .

$u = \frac{- 6}{- 9}$

$u = \frac{- 6}{- 9}$

$u = \frac{- 6}{- 9}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of

$- 6$ and

$- 9$ .

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Step 6.3.1.1

Factor

$- 3$ out of

$- 6$ .

$u = \frac{- 3 (2)}{- 9}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor

$- 3$ out of

$- 9$ .

$u = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Step 6.3.1.2.2

Cancel the common factor.

$u = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Step 6.3.1.2.3

Rewrite the expression.

$u = \frac{2}{3}$

$u = \frac{2}{3}$

$u = \frac{2}{3}$

$u = \frac{2}{3}$

$u = \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$u = \frac{2}{3}$

Decimal Form:

$u = 0.\overline{6}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$