To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 5)(y + 2)
(y x y) + (y x 2) + (5 x y) + (5 x 2)
y² + 2y + 5y + 10
y² + 7y + 10

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -5 as well and sum (Inside, Outside) to equal 4. For this problem, those two numbers are -1 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 4y - 5
y² + (-1 + 5)y + (-1 x 5)
(y - 1)(y + 5)

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

6b + 3z = -7b + z - 2
6b = -7b + z - 2 - 3z
6b + 7b = z - 2 - 3z
13b = -2z - 2
b = \( \frac{-2z - 2}{13} \)
b = \( \frac{-2z}{13} \) + \( \frac{-2}{13} \)
b = -\(\frac{2}{13}\)z - \(\frac{2}{13}\)

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² - 12y + 27 = 0
(y - 3)(y - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 3) or (y - 9) must equal zero:

If (y - 3) = 0, y must equal 3
If (y - 9) = 0, y must equal 9

So the solution is that y = 3 or 9