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

b² + 15b + 56 = 0
(b + 7)(b + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 7) or (b + 8) must equal zero:

If (b + 7) = 0, b must equal -7
If (b + 8) = 0, b must equal -8

So the solution is that b = -7 or -8

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:

z² - 3z - 18 = -z - 3
z² - 3z - 18 + 3 = -z
z² - 3z + z - 15 = 0
z² - 2z - 15 = 0

Next, factor the quadratic equation:

z² - 2z - 15 = 0
(z + 3)(z - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 3) or (z - 5) must equal zero:

If (z + 3) = 0, z must equal -3
If (z - 5) = 0, z must equal 5

So the solution is that z = -3 or 5

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

2a(a - x)
2(6)(6 - 5)
2(6)(1)
(12)(1)
12

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.

-b - 2z = -8b - 6z - 4
-b = -8b - 6z - 4 + 2z
-b + 8b = -6z - 4 + 2z
7b = -4z - 4
b = \( \frac{-4z - 4}{7} \)
b = \( \frac{-4z}{7} \) + \( \frac{-4}{7} \)
b = -\(\frac{4}{7}\)z - \(\frac{4}{7}\)

You need to find the value of b so solve the first equation in terms of y:

5b + y = -5
y = -5 - 5b

then substitute the result (-5 - 5b) into the second equation:

4b - 3(-5 - 5b) = -1
4b + (-3 x -5) + (-3 x -5b) = -1
4b + 15 + 15b = -1
4b + 15b = -1 - 15
19b = -16
b = \( \frac{-16}{19} \)
b = -\(\frac{16}{19}\)