What is the value of x in the equation 4x^2 - 12x + 9 = 0?

What is the value of x in the equation 4x^2 - 12x + 9 = 0?

Step 1: Start with the equation 4x^2 - 12x + 9 = 0.
Step 2: Notice that the equation can be factored. Look for two numbers that multiply to (4 * 9) = 36 and add to -12.
Step 3: The numbers -6 and -6 work because -6 * -6 = 36 and -6 + -6 = -12.
Step 4: Rewrite the equation using these numbers: 4x^2 - 6x - 6x + 9 = 0.
Step 5: Group the terms: (4x^2 - 6x) + (-6x + 9) = 0.
Step 6: Factor out common terms from each group: 2x(2x - 3) - 3(2x - 3) = 0.
Step 7: Now factor out (2x - 3): (2x - 3)(2x - 3) = 0.
Step 8: Set each factor equal to zero: 2x - 3 = 0.
Step 9: Solve for x: 2x = 3, so x = 3/2.
Step 10: Since both factors are the same, the solution is x = 3/2.

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