Question

question
solve for all values of x:
(7x + 6)^2 - 8(7x + 6) = 0
answer attempt 1 out of 2
additional solution no solution
x =
submit answer

Explanation:

Step1: Factor out common term

Let $y = 7x+6$, rewrite equation:
$y^2 - 8y = 0$
Factor: $y(y - 8) = 0$

Step2: Solve for y

Set each factor to 0:
$y = 0$ or $y - 8 = 0 \implies y = 8$

Step3: Substitute back $y=7x+6$

First solution: $7x + 6 = 0$
Second solution: $7x + 6 = 8$

Step4: Solve for x (first case)

$7x = -6 \implies x = \frac{-6}{7}$

Step5: Solve for x (second case)

$7x = 8 - 6 = 2 \implies x = \frac{2}{7}$

Answer:

$x = -\frac{6}{7}$ and $x = \frac{2}{7}$