To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

A trapezoid is a quadrilateral with one set of parallel sides.

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-3a + 10z = 5a - 9z - 9
-3a = 5a - 9z - 9 - 10z
-3a - 5a = -9z - 9 - 10z
-8a = -19z - 9
a = \( \frac{-19z - 9}{-8} \)
a = \( \frac{-19z}{-8} \) + \( \frac{-9}{-8} \)
a = 2\(\frac{3}{8}\)z + 1\(\frac{1}{8}\)