Trigonometry Examples

$7 x + 5 x - 3 y + 54 = 180$

Step 1

Add $7 x$ and $5 x$ .

$12 x - 3 y + 54 = 180$

Step 2

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

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Step 2.1

Add $3 y$ to both sides of the equation.

$12 x + 54 = 180 + 3 y$

Step 2.2

Subtract $54$ from both sides of the equation.

$12 x = 180 + 3 y - 54$

Step 2.3

Subtract $54$ from $180$ .

$12 x = 3 y + 126$

Step 3

Divide each term in $12 x = 3 y + 126$ by $12$ and simplify.

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Step 3.1

Divide each term in $12 x = 3 y + 126$ by $12$ .

$\frac{12 x}{12} = \frac{3 y}{12} + \frac{126}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{3 y}{12} + \frac{126}{12}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{3 y}{12} + \frac{126}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $3$ and $12$ .

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Step 3.3.1.1.1

Factor $3$ out of $3 y$ .

$x = \frac{3 (y)}{12} + \frac{126}{12}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $3$ out of $12$ .

$x = \frac{3 y}{3 \cdot 4} + \frac{126}{12}$

Step 3.3.1.1.2.2

Cancel the common factor.

$x = \frac{3 y}{3 \cdot 4} + \frac{126}{12}$

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{y}{4} + \frac{126}{12}$

Step 3.3.1.2

Cancel the common factor of $126$ and $12$ .

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Step 3.3.1.2.1

Factor $6$ out of $126$ .

$x = \frac{y}{4} + \frac{6 (21)}{12}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $6$ out of $12$ .

$x = \frac{y}{4} + \frac{6 \cdot 21}{6 \cdot 2}$

Step 3.3.1.2.2.2

Cancel the common factor.

$x = \frac{y}{4} + \frac{6 \cdot 21}{6 \cdot 2}$

Step 3.3.1.2.2.3

Rewrite the expression.

$x = \frac{y}{4} + \frac{21}{2}$