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 -36 as well and sum (Inside, Outside) to equal -5. For this problem, those two numbers are -9 and 4. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 5y - 36
y² + (-9 + 4)y + (-9 x 4)
(y - 9)(y + 4)

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.

8b - 5x = b + 7x - 6
8b = b + 7x - 6 + 5x
8b - b = 7x - 6 + 5x
7b = 12x - 6
b = \( \frac{12x - 6}{7} \)
b = \( \frac{12x}{7} \) + \( \frac{-6}{7} \)
b = 1\(\frac{5}{7}\)x - \(\frac{6}{7}\)

An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

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.

6a⁶ - 4a⁶ = 2a⁶

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

-6a - 4 < 9 + 4a
-6a < 9 + 4a + 4
-6a - 4a < 9 + 4
-10a < 13
a < \( \frac{13}{-10} \)
a < -1\(\frac{3}{10}\)