x²-2x-15<0

To solve the inequality x²-2x-15<0, we can use the method of factoring.

Step 1: Factor the quadratic expression on the left side of the inequality. x²-2x-15 = (x-5)(x+3)

Step 2: Set each factor equal to zero and solve for x. x-5 = 0, x = 5 x+3 = 0, x = -3

Step 3: Create a sign chart to determine the intervals where the quadratic expression is positive and negative. x | -∞ | -3 | 5 | +∞ (x-5) | - | - | + | + (x+3) | - | - | - | +

Step 4: Analyze the sign chart to identify the intervals where the expression is less than zero, which is the solution to the inequality. x < -3 or 5 < x

Therefore, the solution to the inequality x²-2x-15<0 is x < -3 or x > 5.