When solving quadratic equations, if the equation is not set equal to zero, first manipulate the equation so that it is set equal to zero: ax^{2} + bx + c = 0. Then, factor the quadratic and, because it's set to zero, you know that one of the factors must equal zero for the equation to equal zero. Finding the value that will make each factor, i.e. (x + ?), equal to zero will give you the possible value(s) of x.

Solve for z:

z^{2} + 4z - 1 = 3z + 1

2 or -5 | |

8 or 7 | |

1 or -2 | |

6 or 1 |