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

z² + 3z - 10 = 0
(z - 2)(z + 5) = 0

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

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

So the solution is that z = 2 or -5

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 8cm + 6cm + 12cm = 26cm

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.

-5c + 2 < \( \frac{c}{4} \)
4 x (-5c + 2) < c
(4 x -5c) + (4 x 2) < c
-20c + 8 < c
-20c + 8 - c < 0
-20c - c < -8
-21c < -8
c < \( \frac{-8}{-21} \)
c < \(\frac{8}{21}\)

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 - 4a = 0a

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 -10 as well and sum (Inside, Outside) to equal -3. For this problem, those two numbers are -5 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 3y - 10
y² + (-5 + 2)y + (-5 x 2)
(y - 5)(y + 2)