Answer:
Expanded: 4x² - 4x - 168 = 0
Solutions: x = -6, 7
Step-by-step explanation:
If you need to expand the expression:
First, distribute the 4 to the binomial directly to its right but multiply each term within the parentheses by 4.
4(x - 7) = 4(x) + 4(-7) = 4x - 28
The new equation is (4x - 28)(x + 6) = 0
Next, we use the FOIL method. This is an acronym that instructs which terms in each binomial are multiplied together. It stands for Firsts, Outsides, Insides, and Lasts.
Firsts: 4x(x) = 4x²
Outsides: 4x(6) = 24x
Insides: -28(x) = -28x
Lasts: -28(6) = -168
Put them into one equation and combine like terms.
4x² + 24x - 28x - 168 = 0
4x² - 4x - 168 = 0
If you need solutions to the expression:
First, divide both sides of the equation of the 4 that was previous factored out.
4(x - 7)(x + 6) = 0
[4(x - 7)(x + 6)] / 4 = 0 / 4
(x - 7)(x + 6) = 0
Now, set each binomial equal to 0 and solve for x using whatever operations are necessary.
x - 7 = 0 x + 6 = 0
x - 7 + 7 = 0 + 7 x + 6 - 6 = 0 - 6
x + 0 = 7 x + 0 = - 6
x = 7 x = - 6
The solutions to the expression are x = -6, 7