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

y² + 12y + 32 = 0
(y + 4)(y + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 4) or (y + 8) must equal zero:

If (y + 4) = 0, y must equal -4
If (y + 8) = 0, y must equal -8

So the solution is that y = -4 or -8

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

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 + 3y = -5a - 4y + 6
a = -5a - 4y + 6 - 3y
a + 5a = -4y + 6 - 3y
6a = -7y + 6
a = \( \frac{-7y + 6}{6} \)
a = \( \frac{-7y}{6} \) + \( \frac{6}{6} \)
a = -1\(\frac{1}{6}\)y + 1

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 4 x 2 = \( \frac{8}{2} \) = 4