(x+3)(x+4)=0 Solve

2 min read Jun 16, 2024

Solving the Equation (x+3)(x+4) = 0

This equation represents a simple quadratic equation in factored form. To solve for the value(s) of x that satisfy the equation, we can utilize the Zero Product Property.

The Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero. In simpler terms, if a * b = 0*, then either a = 0 or b = 0 (or both).

Applying the Property

In our equation, (x+3)(x+4) = 0, we have two factors: (x+3) and (x+4). To satisfy the Zero Product Property, either:

(x+3) = 0 or
(x+4) = 0

Solving for x

Now, let's solve each equation separately:

(x+3) = 0
- Subtract 3 from both sides: x = -3
(x+4) = 0
- Subtract 4 from both sides: x = -4

Solutions

Therefore, the solutions to the equation (x+3)(x+4) = 0 are x = -3 and x = -4.

Verification

We can verify these solutions by substituting them back into the original equation:

For x = -3: (-3 + 3)(-3 + 4) = (0)(1) = 0
For x = -4: (-4 + 3)(-4 + 4) = (-1)(0) = 0

Both solutions satisfy the equation, confirming our results.