(x-5)(7x-21)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-5)(7x-21) = 0

This equation represents a quadratic equation in factored form. To solve for x, we can use the Zero Product Property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve it:

1. Set each factor equal to zero:

   • x - 5 = 0
   • 7x - 21 = 0

2. Solve for x in each equation:

   • x = 5
   • 7x = 21
   • x = 3

Therefore, the solutions to the equation (x-5)(7x-21) = 0 are x = 5 and x = 3.

Explanation:

The equation represents a parabola that intersects the x-axis at two points, x = 5 and x = 3. These points are the roots of the equation, meaning they are the values of x that make the equation true.

In general, to solve equations in factored form, follow these steps:

1. Factor the equation completely.
2. Set each factor equal to zero.
3. Solve for the variable in each equation.
4. The solutions are the values of the variable that make the equation true.

By understanding the Zero Product Property and factoring, you can efficiently solve a wide range of quadratic equations.