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.

The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:

c = πd
c = π(2 * r)
c = π(2 * 12)
c = 24π

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(2a)(9ab) + (2a²)(6b)
(2 x 9)(a x a x b) + (2 x 6)(a² x b)
(18)(a¹⁺¹ x b) + (12)(a²b)
18a²b + 12a²b
30a²b

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.

4z - 8 < 3 - 2z
4z < 3 - 2z + 8
4z + 2z < 3 + 8
6z < 11
z < \( \frac{11}{6} \)
z < 1\(\frac{5}{6}\)

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 15 as well and sum (Inside, Outside) to equal -8. For this problem, those two numbers are -5 and -3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 8y + 15
y² + (-5 - 3)y + (-5 x -3)
(y - 5)(y - 3)