Factorise and solve The question 3x²-11x=6

Let's solve the quadratic equation step by step.

Given equation:
\[
3x^2 - 11x = 6
\]

### Step 1: Rearrange the equation
Move all terms to one side:
\[
3x^2 - 11x - 6 = 0
\]

### Step 2: Factorise the quadratic expression
We need to factor the expression \(3x^2 - 11x - 6\). To do this, look for two numbers that multiply to \(3 \times -6 = -18\) and add to \(-11\). These numbers are \(-9\) and \(2\).

So, we can split the middle term \(-11x\) into \(-9x + 2x\):
\[
3x^2 - 9x + 2x - 6 = 0
\]

### Step 3: Group the terms
Now group the terms:
\[
(3x^2 - 9x) + (2x - 6) = 0
\]

Factor out the common factors in each group:
\[
3x(x - 3) + 2(x - 3) = 0
\]

### Step 4: Factor out the common binomial
Now factor out \((x - 3)\):
\[
(3x + 2)(x - 3) = 0
\]

### Step 5: Solve for \(x\)
Set each factor equal to zero:
1. \(3x + 2 = 0\) gives \(x = -\frac{2}{3}\)
2. \(x - 3 = 0\) gives \(x = 3\)

Thus, the solutions are:
\[
x = -\frac{2}{3}, \quad x = 3
\]

Would you like further details on any of the steps? Here are some related questions for practice:

1. How would you factorise \(2x^2 - 5x - 3 = 0\)?
2. Solve \(x^2 - 7x + 12 = 0\).
3. What is the quadratic formula used for solving any quadratic equation?
4. How do you factor \(6x^2 - 13x + 6 = 0\)?
5. Explain the process of completing the square for a quadratic equation.

**Tip**: Always check your factorisation by expanding the factors back to ensure the result matches the original equation.

Factorise and solve the question 3x² - 11x = 6.

Learn how to factor and solve the quadratic equation 3x² - 11x = 6 with a detailed step-by-step solution. This problem focuses on factoring techniques, including grouping and using the zero product property, making it suitable for students in Grades 9-10.

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