Quadratic equation by factoring 7x²+18x=10x²+12x

To solve the quadratic equation by factoring, we first need to bring all the terms to one side of the equation to set it equal to zero. Here is the given equation:

\[ 7x^2 + 18x = 10x^2 + 12x \]

First, let's move all terms to one side of the equation:

\[ 7x^2 + 18x - 10x^2 - 12x = 0 \]

Combine like terms:

\[ (7x^2 - 10x^2) + (18x - 12x) = 0 \]

\[ -3x^2 + 6x = 0 \]

Now, factor out the greatest common factor (GCF):

\[ -3x(x - 2) = 0 \]

To find the solutions, set each factor equal to zero:

1. \( -3x = 0 \)
2. \( x - 2 = 0 \)

Solving these equations, we get:

1. \( x = 0 \)
2. \( x = 2 \)

Therefore, the solutions to the quadratic equation \( 7x^2 + 18x = 10x^2 + 12x \) are \( x = 0 \) and \( x = 2 \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How can you verify the solutions to the quadratic equation?
2. What is the significance of factoring in solving quadratic equations?
3. How do you solve quadratic equations using the quadratic formula?
4. Can all quadratic equations be factored easily?
5. What are the differences between factoring and using the quadratic formula?
6. How do you complete the square to solve quadratic equations?
7. What are the applications of solving quadratic equations in real life?
8. How does the discriminant of a quadratic equation determine the nature of its roots?

**Tip:** Always check your factored form by multiplying the factors to see if you get back to the original equation. This helps verify that the factoring is done correctly.

Learn how to solve the quadratic equation 7x² + 18x = 10x² + 12x step-by-step using factoring. This problem involves algebraic concepts such as quadratic equations, factoring, and the zero product property theorem. Suitable for students in Grades 9-12.

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