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

-2c - 5z = 9c + 3z - 1
-2c = 9c + 3z - 1 + 5z
-2c - 9c = 3z - 1 + 5z
-11c = 8z - 1
c = \( \frac{8z - 1}{-11} \)
c = \( \frac{8z}{-11} \) + \( \frac{-1}{-11} \)
c = -\(\frac{8}{11}\)z + \(\frac{1}{11}\)

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

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, \(c = \sqrt{a + b}\)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² + 9b + 32 = -2b + 2
b² + 9b + 32 - 2 = -2b
b² + 9b + 2b + 30 = 0
b² + 11b + 30 = 0

Next, factor the quadratic equation:

b² + 11b + 30 = 0
(b + 5)(b + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 5) or (b + 6) must equal zero:

If (b + 5) = 0, b must equal -5
If (b + 6) = 0, b must equal -6

So the solution is that b = -5 or -6

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 51° - 38° = 91°