(2x-6)*(x^2+7x+10)=0

2 min read Jun 16, 2024

Solving the Equation: (2x-6)(x^2+7x+10) = 0

This equation is a quadratic equation in factored form. To solve it, we can use the Zero Product Property:

Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.

Applying this to our equation:

Factor the quadratic expression: The quadratic expression (x^2 + 7x + 10) can be factored as (x + 2)(x + 5).
Set each factor to zero: This gives us two equations:
- 2x - 6 = 0
- (x + 2)(x + 5) = 0
Solve for x in each equation:
- For 2x - 6 = 0:
  - Add 6 to both sides: 2x = 6
  - Divide both sides by 2: x = 3
- For (x + 2)(x + 5) = 0:
  - Apply the Zero Product Property again:
    - x + 2 = 0 or x + 5 = 0
  - Solve for x in each equation:
    - x = -2 or x = -5

Therefore, the solutions to the equation (2x-6)(x^2+7x+10) = 0 are x = 3, x = -2, and x = -5.