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The equation given is:

\[
2x^2 + 3x - 20 = 0
\]

We need to solve this quadratic equation by factorization. Let's break it down step by step:

### Step 1: Multiply the coefficient of \(x^2\) (which is 2) with the constant term (which is -20).
\[
2 \times (-20) = -40
\]
We need to find two numbers that multiply to give \(-40\) and add to give the middle term coefficient, which is \(+3\).

The two numbers are \(+8\) and \(-5\), because:
\[
8 \times (-5) = -40 \quad \text{and} \quad 8 + (-5) = 3
\]

### Step 2: Rewrite the middle term using these two numbers.
\[
2x^2 + 8x - 5x - 20 = 0
\]

### Step 3: Factor by grouping.
Group the terms in pairs:
\[
(2x^2 + 8x) - (5x + 20) = 0
\]
Factor out the greatest common factor from each group:
\[
2x(x + 4) - 5(x + 4) = 0
\]

### Step 4: Factor out the common binomial factor.
\[
(2x - 5)(x + 4) = 0
\]

### Step 5: Solve for \(x\) by setting each factor equal to 0.

1. \(2x - 5 = 0 \implies x = \frac{5}{2}\)
2. \(x + 4 = 0 \implies x = -4\)

### Final Answer:
The solutions are:
\[
x = \frac{5}{2} \quad \text{or} \quad x = -4
\]

Would you like a detailed explanation of any step?

Here are 5 related questions to explore:

1. How do you factor more complex quadratic equations?
2. What is the quadratic formula, and how does it compare to factorization?
3. Can all quadratic equations be solved by factorization?
4. How can you verify the solutions to a quadratic equation?
5. What happens if a quadratic equation has no real solutions?

**Tip**: Always double-check your factor pairs to ensure that both their product and sum match the necessary values.

Solve by factorisation: 2x^2 + 3x - 20 = 0

Learn how to solve the quadratic equation 2x^2 + 3x - 20 = 0 using factorization. This problem covers key algebraic concepts such as quadratic equations, factorization methods, and the zero-product property. Suitable for students in Grades 8-10.

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