(3x%2B12)%3D0.jpeg "(2x−10)(3x+12)=0")
Solving the Equation (2x - 10)(3x + 12) = 0
This equation is a quadratic equation in factored form. We can use the Zero Product Property to solve it. 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.
Steps to Solve:
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Set each factor equal to zero:
- 2x - 10 = 0
- 3x + 12 = 0
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Solve for x in each equation:
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For 2x - 10 = 0:
- Add 10 to both sides: 2x = 10
- Divide both sides by 2: x = 5
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For 3x + 12 = 0:
- Subtract 12 from both sides: 3x = -12
- Divide both sides by 3: x = -4
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Solution:
The solutions to the equation (2x - 10)(3x + 12) = 0 are x = 5 and x = -4.
Verification:
We can verify our solutions by substituting them back into the original equation:
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For x = 5:
- (2(5) - 10)(3(5) + 12) = (10 - 10)(15 + 12) = (0)(27) = 0
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For x = -4:
- (2(-4) - 10)(3(-4) + 12) = (-8 - 10)(-12 + 12) = (-18)(0) = 0
Therefore, both solutions satisfy the original equation.
In Conclusion:
The equation (2x - 10)(3x + 12) = 0 has two solutions: x = 5 and x = -4. This was solved using the Zero Product Property, which allowed us to set each factor equal to zero and solve for x.