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:

a² + 7a - 6 = 5a + 2
a² + 7a - 6 - 2 = 5a
a² + 7a - 5a - 8 = 0
a² + 2a - 8 = 0

Next, factor the quadratic equation:

a² + 2a - 8 = 0
(a - 2)(a + 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 2) or (a + 4) must equal zero:

If (a - 2) = 0, a must equal 2
If (a + 4) = 0, a must equal -4

So the solution is that a = 2 or -4

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 + 5x = -9a - 3x + 2
3a = -9a - 3x + 2 - 5x
3a + 9a = -3x + 2 - 5x
12a = -8x + 2
a = \( \frac{-8x + 2}{12} \)
a = \( \frac{-8x}{12} \) + \( \frac{2}{12} \)
a = -\(\frac{2}{3}\)x + \(\frac{1}{6}\)

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.

9a - 7a = 2a

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 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.)

4c(c - x)
4(-8)(-8 + 9)
4(-8)(1)
(-32)(1)
-32