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 + 4z - 1 = z + 3
z² + 4z - 1 - 3 = z
z² + 4z - z - 4 = 0
z² + 3z - 4 = 0

Next, factor the quadratic equation:

z² + 3z - 4 = 0
(z - 1)(z + 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 1) or (z + 4) must equal zero:

If (z - 1) = 0, z must equal 1
If (z + 4) = 0, z must equal -4

So the solution is that z = 1 or -4

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 2² + 8²
c² = 4 + 64
c² = 68
c = \( \sqrt{68} \)

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.

7a - 8a = -1a

When solving an equation with two variables, 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.)

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

y² - 3y - 40 = 0
(y + 5)(y - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 5) or (y - 8) must equal zero:

If (y + 5) = 0, y must equal -5
If (y - 8) = 0, y must equal 8

So the solution is that y = -5 or 8