Basic Math Examples

$0.09 = \frac{3}{5} \cdot ((0.055) (1 - 0.35)) + \frac{2}{5} (K)$

Step 1

Rewrite the equation as $\frac{3}{5} \cdot (0.055 (1 - 0.35)) + \frac{2}{5} K = 0.09$ .

$\frac{3}{5} \cdot (0.055 (1 - 0.35)) + \frac{2}{5} K = 0.09$

Step 2

Simplify each term.

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Step 2.1

Subtract $0.35$ from $1$ .

$\frac{3}{5} \cdot (0.055 \cdot 0.65) + \frac{2}{5} K = 0.09$

Step 2.2

Multiply $0.055$ by $0.65$ .

$\frac{3}{5} \cdot 0.03575 + \frac{2}{5} K = 0.09$

Step 2.3

Multiply $\frac{3}{5} \cdot 0.03575$ .

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Step 2.3.1

Combine $\frac{3}{5}$ and $0.03575$ .

$\frac{3 \cdot 0.03575}{5} + \frac{2}{5} K = 0.09$

Step 2.3.2

Multiply $3$ by $0.03575$ .

$\frac{0.10725}{5} + \frac{2}{5} K = 0.09$

Step 2.4

Divide $0.10725$ by $5$ .

$0.02145 + \frac{2}{5} K = 0.09$

Step 2.5

Combine $\frac{2}{5}$ and $K$ .

$0.02145 + \frac{2 K}{5} = 0.09$

Step 3

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

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Step 3.1

Subtract $0.02145$ from both sides of the equation.

$\frac{2 K}{5} = 0.09 - 0.02145$

Step 3.2

Subtract $0.02145$ from $0.09$ .

$\frac{2 K}{5} = 0.06855$

Step 4

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 K}{5} = \frac{5}{2} \cdot 0.06855$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{2} \cdot \frac{2 K}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 K}{5} = \frac{5}{2} \cdot 0.06855$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 K) = \frac{5}{2} \cdot 0.06855$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 K$ .

$\frac{1}{2} (2 (K)) = \frac{5}{2} \cdot 0.06855$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 K) = \frac{5}{2} \cdot 0.06855$

Step 5.1.1.2.3

Rewrite the expression.

$K = \frac{5}{2} \cdot 0.06855$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{2} \cdot 0.06855$ .

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Step 5.2.1.1

Multiply $\frac{5}{2} \cdot 0.06855$ .

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Step 5.2.1.1.1

Combine $\frac{5}{2}$ and $0.06855$ .

$K = \frac{5 \cdot 0.06855}{2}$

Step 5.2.1.1.2

Multiply $5$ by $0.06855$ .

$K = \frac{0.34275}{2}$

Step 5.2.1.2

Divide $0.34275$ by $2$ .

$K = 0.171375$