Solve for all values of x : (6x+5)^(2)+(6x+5)=0 Answer: x=

Set up equation: Set up the equation to solve for x. We are given the equation (6x+5)^(2)+(6x+5)=0. To solve for x, we need to find the values of x that satisfy this equation.Factor out common term: Factor out the common term (6x+5). Notice that (6x+5) is a common term in both parts of the equation. We can factor it out to simplify the equation: (6x+5)((6x+5)+1) = 0Simplify factored equation: Simplify the factored equation. Now we simplify the equation by expanding the second term: (6x+5)(6x+5+1) = 0 (6x+5)(6x+6) = 0Set factors equal: Set each factor equal to zero and solve for x. Since the product of two factors is zero, at least one of the factors must be zero. We set each factor equal to zero and solve for x: 6x+5 = 0 or 6x+6 = 0Solve first equation: Solve the first equation for x. 6x+5 = 0 6x = -5 x = -5/6Solve second equation: Solve the second equation for x. 6x+6 = 0 6x = -6 x = -6/6 x = -1

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Solve for all values of
x :

(6x+5)^(2)+(6x+5)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $(6 x+5)^{2}+(6 x+5)=0$ $\newline$ Answer: $x=$

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Algebra 2

Composition of linear and quadratic functions: find an equation

Full solution

Q. Solve for all values of

x

\newline

(6 x+5)^{2}+(6 x+5)=0

\newline

Answer:

x=

Set up equation: Set up the equation to solve for $x$ . We are given the equation $(6x+5)^{2}+(6x+5)=0$ . To solve for $x$ , we need to find the values of $x$ that satisfy this equation.
Factor out common term: Factor out the common term $(6x+5)$ . Notice that $(6x+5)$ is a common term in both parts of the equation. We can factor it out to simplify the equation: $(6x+5)((6x+5)+1) = 0$
Simplify factored equation: Simplify the factored equation. $\newline$ Now we simplify the equation by expanding the second term: $\newline$ $(6x+5)(6x+5+1) = 0$ $\newline$ $(6x+5)(6x+6) = 0$
Set factors equal: Set each factor equal to zero and solve for $x$ . Since the product of two factors is zero, at least one of the factors must be zero. We set each factor equal to zero and solve for $x$ : $6x+5 = 0$ or $6x+6 = 0$
Solve first equation: Solve the first equation for $x$ . $6x+5 = 0$ $6x = -5$ $x = -\frac{5}{6}$
Solve second equation: Solve the second equation for $x$ . $6x+6 = 0$ $6x = -6$ $x = -6/6$ $x = -1$