Solve for all values of x : (3x-2)^(2)+5(3x-2)=0 Answer: x=

Denote u = 3x - 2: Let's denote u = 3x - 2 to simplify the equation. The equation becomes: u^2 + 5u = 0Factor out u: Now, factor out u from the equation: u(u + 5) = 0Set factors equal to zero: Set each factor equal to zero to find the solutions for u: u = 0 or u + 5 = 0Solve for u: Solve for u in each case: u = 0 or u = -5Substitute back for u: Now, substitute back 3x - 2 for u to find the values of x: 3x - 2 = 0 or 3x - 2 = -5Solve for x: Solve each equation for x: For 3x - 2 = 0, we get x = 2/3. For 3x - 2 = -5, we get x = -1.

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Solve for all values of
x :

(3x-2)^(2)+5(3x-2)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $(3 x-2)^{2}+5(3 x-2)=0$ $\newline$ Answer: $x=$

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Solve for all values of

x

\newline

(3 x-2)^{2}+5(3 x-2)=0

\newline

Answer:

x=

Denote $u = 3x - 2$ : Let's denote $u = 3x - 2$ to simplify the equation. The equation becomes: $u^2 + 5u = 0$
Factor out $u$ : Now, factor out $u$ from the equation: $u(u + 5) = 0$
Set factors equal to zero: Set each factor equal to zero to find the solutions for $u$ : $u = 0$ or $u + 5 = 0$
Solve for u: Solve for u in each case: $\newline$ $u = 0$ or $u = -5$
Substitute back for u: Now, substitute back $3x - 2$ for $u$ to find the values of $x$ : $\newline$ $3x - 2 = 0$ or $3x - 2 = -5$
Solve for x: Solve each equation for x: $\newline$ For $3x - 2 = 0$ , we get $x = \frac{2}{3}$ . $\newline$ For $3x - 2 = -5$ , we get $x = -1$ .