Expand Left Side: Expand the left side of the equation (3s+1)(s-4). We distribute each term in the first parenthesis by each term in the second parenthesis. (3s+1)(s-4) = 3s(s) + 3s(-4) + 1(s) + 1(-4)Simplify Expanded Expression: Simplify the expanded expression. 3s(s) + 3s(-4) + 1(s) + 1(-4) = 3s^2 - 12s + s - 4 Combine like terms. 3s^2 - 12s + s - 4 = 3s^2 - 11s - 4Combine Like Terms: Expand the right side of the equation -5(s-1). We distribute -5 to each term inside the parenthesis. -5(s-1) = -5s + 5Expand Right Side: Set the expanded left side equal to the expanded right side. 3s^2 - 11s - 4 = -5s + 5Set Equation Equal: Move all terms to one side to set the equation to zero. Add 5s to both sides and subtract 5 from both sides. 3s^2 - 11s + 5s - 4 - 5 = 0 Combine like terms. 3s^2 - 6s - 9 = 0

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

(3 s+1)(s-4)=-5(s-1)

Expand Left Side: Expand the left side of the equation $(3s+1)(s-4)$ . We distribute each term in the first parenthesis by each term in the second parenthesis. $(3s+1)(s-4) = 3s(s) + 3s(-4) + 1(s) + 1(-4)$
Simplify Expanded Expression: Simplify the expanded expression. $\newline$ $3s(s) + 3s(-4) + 1(s) + 1(-4) = 3s^2 - 12s + s - 4$ $\newline$ Combine like terms. $\newline$ $3s^2 - 12s + s - 4 = 3s^2 - 11s - 4$
Combine Like Terms: Expand the right side of the equation $-5(s-1)$ . $\newline$ We distribute $-5$ to each term inside the parenthesis. $\newline$ $-5(s-1) = -5s + 5$
Expand Right Side: Set the expanded left side equal to the expanded right side. $\newline$ $3s^2 - 11s - 4 = -5s + 5$
Set Equation Equal: Move all terms to one side to set the equation to zero. $\newline$ Add $5s$ to both sides and subtract $5$ from both sides. $\newline$ $3s^2 - 11s + 5s - 4 - 5 = 0$ $\newline$ Combine like terms. $\newline$ $3s^2 - 6s - 9 = 0$