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

Factor out common term: Factor out the common term (x+3) from the equation. We have the equation (x+3)² - (x+3) = 0. Notice that (x+3) is a common term in both parts of the equation. We can factor it out to simplify the equation. (x+3)((x+3) - 1) = 0 (x+3)(x+3 - 1) = 0 (x+3)(x+2) = 0Apply zero-product property: Apply the zero-product property. If the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x. (x+3) = 0 or (x+2) = 0Solve first equation: Solve the first equation for x. (x+3) = 0 Subtract 3 from both sides to isolate x. x = -3Solve second equation: Solve the second equation for x. (x+2) = 0 Subtract 2 from both sides to isolate x. x = -2

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Solve for all values of
x :

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

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

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Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Solve for all values of

x

\newline

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

\newline

Answer:

x=

Factor out common term: Factor out the common term $(x+3)$ from the equation. $\newline$ We have the equation $(x+3)^2 - (x+3) = 0$ . Notice that $(x+3)$ is a common term in both parts of the equation. We can factor it out to simplify the equation. $\newline$ $(x+3)((x+3) - 1) = 0$ $\newline$ $(x+3)(x+3 - 1) = 0$ $\newline$ $(x+3)(x+2) = 0$
Apply zero-product property: Apply the zero-product property. $\newline$ If the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for $x$ . $\newline$ $(x+3) = 0$ or $(x+2) = 0$
Solve first equation: Solve the first equation for $x$ . $(x+3) = 0$ Subtract $3$ from both sides to isolate $x$ . $x = -3$
Solve second equation: Solve the second equation for $x$ . $(x+2) = 0$ Subtract $2$ from both sides to isolate $x$ . $x = -2$