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 -5 and 1. Then, plug these into a set of binomials using the square root of the First variable (y²):

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

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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 expression that's not set to zero is to solve the equation so that it is set to zero:

c² - 14c + 39 = -c - 1
c² - 14c + 39 + 1 = -c
c² - 14c + c + 40 = 0
c² - 13c + 40 = 0

Next, factor the quadratic equation:

c² - 13c + 40 = 0
(c - 5)(c - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 5) or (c - 8) must equal zero:

If (c - 5) = 0, c must equal 5
If (c - 8) = 0, c must equal 8

So the solution is that c = 5 or 8

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.

5a⁷ - 7a⁷ = -2a⁷