Algebra Examples

$3 a b - 15 b - 7 a + 35 = 0$

Step 1

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

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Step 1.1

Add $7 a$ to both sides of the equation.

$3 a b - 15 b + 35 = 7 a$

Step 1.2

Subtract $35$ from both sides of the equation.

$3 a b - 15 b = 7 a - 35$

Step 2

Factor $3 b$ out of $3 a b - 15 b$ .

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Step 2.1

Factor $3 b$ out of $3 a b$ .

$3 b (a) - 15 b = 7 a - 35$

Step 2.2

Factor $3 b$ out of $- 15 b$ .

$3 b (a) + 3 b (- 5) = 7 a - 35$

Step 2.3

Factor $3 b$ out of $3 b (a) + 3 b (- 5)$ .

$3 b (a - 5) = 7 a - 35$

Step 3

Divide each term in $3 b (a - 5) = 7 a - 35$ by $3 (a - 5)$ and simplify.

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Step 3.1

Divide each term in $3 b (a - 5) = 7 a - 35$ by $3 (a - 5)$ .

$\frac{3 b (a - 5)}{3 (a - 5)} = \frac{7 a}{3 (a - 5)} + \frac{- 35}{3 (a - 5)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 b (a - 5)}{3 (a - 5)} = \frac{7 a}{3 (a - 5)} + \frac{- 35}{3 (a - 5)}$

Step 3.2.1.2

Rewrite the expression.

$\frac{b (a - 5)}{a - 5} = \frac{7 a}{3 (a - 5)} + \frac{- 35}{3 (a - 5)}$

Step 3.2.2

Cancel the common factor of $a - 5$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{b (a - 5)}{a - 5} = \frac{7 a}{3 (a - 5)} + \frac{- 35}{3 (a - 5)}$

Step 3.2.2.2

Divide $b$ by $1$ .

$b = \frac{7 a}{3 (a - 5)} + \frac{- 35}{3 (a - 5)}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$b = \frac{7 a}{3 (a - 5)} - \frac{35}{3 (a - 5)}$