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.

-3a - 6z = a - 4z + 6
-3a = a - 4z + 6 + 6z
-3a - a = -4z + 6 + 6z
-4a = 2z + 6
a = \( \frac{2z + 6}{-4} \)
a = \( \frac{2z}{-4} \) + \( \frac{6}{-4} \)
a = -\(\frac{1}{2}\)z - 1\(\frac{1}{2}\)

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.

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(6a)(4ab) + (2a²)(5b)
(6 x 4)(a x a x b) + (2 x 5)(a² x b)
(24)(a¹⁺¹ x b) + (10)(a²b)
24a²b + 10a²b
34a²b

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 63 as well and sum (Inside, Outside) to equal 16. For this problem, those two numbers are 7 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 16y + 63
y² + (7 + 9)y + (7 x 9)
(y + 7)(y + 9)

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

a = ½bh
a = ½ x 3 x 4 = \( \frac{12}{2} \) = 6