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

x² + 15x + 56 = 0
(x + 7)(x + 8) = 0

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

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

So the solution is that x = -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:

y² - 3y - 18 = -y - 3
y² - 3y - 18 + 3 = -y
y² - 3y + y - 15 = 0
y² - 2y - 15 = 0

Next, factor the quadratic equation:

y² - 2y - 15 = 0
(y + 3)(y - 5) = 0

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

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

So the solution is that y = -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 - y)
2(6)(6 - 5)
2(6)(1)
(12)(1)
12

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-a - 2y = -8a - 6y - 4
-a = -8a - 6y - 4 + 2y
-a + 8a = -6y - 4 + 2y
7a = -4y - 4
a = \( \frac{-4y - 4}{7} \)
a = \( \frac{-4y}{7} \) + \( \frac{-4}{7} \)
a = -\(\frac{4}{7}\)y - \(\frac{4}{7}\)

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

5a + y = -5
y = -5 - 5a

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

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