Answer: The correct option is B.
Step-by-step explanation:
(x+5)(2x-1)=3(x+5)
Multiply the parentheses
2x^2 - x + 10x - 5 = 3x + 15
Collect like terms
2x^2 + 9x - 5 = 3x + 15
Move the expression to the left hand side and change its sign, then equate it to 0
2x^2 + 9x - 5 - 3x -15 = 0
Collect like terms
2x^2 + 6x - 20 = 0
Divide each term of the equation by 2
x^2 + 3x - 10 = 0
Rewrite the expression in factorized form
x^2 + 5x - 2x - 10 = 0
Factor the expression
x(x + 5) - 2(x + 5) = 0
(x + 5) (x - 2) = 0
Separate into possible cases but when the product of factors equals 0, at least one factor is 0.
x + 5 = 0———equation (1)
x - 2 = 0———-equation (2)
Solve the equations
x + 5 = 0———equation (1)
Make x the subject
x = 0 - 5
x = -5
x - 2 = 0———equation (2)
Make x the subject
x = 0 + 2
x = 2
Hence, the possible values of x are -5 and 2.