Solve for t 3t^2-12t+9=0

Problem

3*t2−12*t+9=0

Solution

1. Divide the entire equation by the greatest common factor, which is 3 to simplify the coefficients.

t2−4*t+3=0

2. Identify two numbers that multiply to 3 and add to −4 to factor the quadratic expression.

−3×−1=3

−3+(−1)=−4

3. Factor the quadratic equation using the identified numbers.

(t−3)*(t−1)=0

4. Apply the zero product property by setting each factor equal to zero.

t−3=0

t−1=0

5. Solve for t in each linear equation.

t=3

t=1

Final Answer

t=1,3

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