Final answer:
To solve the equation (3x + 2)^2+7(3x+2)-8=0 using substitution, let a = (3x + 2). Solving for a, we get a^2 + 7a - 8 = 0. By factoring, we find two values for a, which can be substituted back to find the possible values of x.
Step-by-step explanation:
To solve the equation (3x + 2)^2+7(3x+2)-8=0 using substitution, we can let a = (3x + 2). By substituting this value, the equation becomes a^2 + 7a - 8 = 0. Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have (a + 8)(a - 1) = 0. Therefore, a = -8 or a = 1. Since we defined a = (3x + 2), we can substitute these values back into the equation to find the possible values of x.
For a = -8, we have (3x + 2) = -8. Solving for x, we get 3x = -10 and x = -10/3.
For a = 1, we have (3x + 2) = 1. Solving for x, we get 3x = -1 and x = -1/3.
Learn more about Solving equations using substitution