(3x-7)%3D0.jpeg "(2x+3)(3x-7)=0")
Solving the Equation (2x + 3)(3x - 7) = 0
This equation is a quadratic equation in factored form. Let's understand how to solve it:
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 our equation, we have two factors: (2x + 3) and (3x - 7). Therefore, for the product to be zero, at least one of these factors must be equal to zero.
Solving for x
Let's set each factor equal to zero and solve for x:
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Factor 1: 2x + 3 = 0
- Subtract 3 from both sides: 2x = -3
- Divide both sides by 2: x = -3/2
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Factor 2: 3x - 7 = 0
- Add 7 to both sides: 3x = 7
- Divide both sides by 3: x = 7/3
Solutions
Therefore, the solutions to the equation (2x + 3)(3x - 7) = 0 are:
- x = -3/2
- x = 7/3
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = -3/2:
- (2(-3/2) + 3)(3(-3/2) - 7) = (0)(-19/2) = 0
- For x = 7/3:
- (2(7/3) + 3)(3(7/3) - 7) = (23/3)(0) = 0
Since both solutions make the equation true, we have confirmed that our solutions are correct.