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:

y² + 11y + 15 = 4y + 5
y² + 11y + 15 - 5 = 4y
y² + 11y - 4y + 10 = 0
y² + 7y + 10 = 0

Next, factor the quadratic equation:

y² + 7y + 10 = 0
(y + 2)(y + 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 2) or (y + 5) must equal zero:

If (y + 2) = 0, y must equal -2
If (y + 5) = 0, y must equal -5

So the solution is that y = -2 or -5

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 -72 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -8 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 72
y² + (-8 + 9)y + (-8 x 9)
(y - 8)(y + 9)

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 area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 7 x 3 = \( \frac{21}{2} \) = 10\(\frac{1}{2}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

4a + 6a = 10a