Solve for t (t-1)(t-4)=(t+1)^2

Problem

(t−1)*(t−4)=(t+1)2

Solution

1. Expand the left side of the equation using the FOIL method.

(t−1)*(t−4)=t2−4*t−t+4

t2−5*t+4

2. Expand the right side of the equation using the square of a binomial formula.

(t+1)2=t2+2*t+1

3. Equate the expanded expressions.

t2−5*t+4=t2+2*t+1

4. Subtract t2 from both sides to simplify the equation.

−5*t+4=2*t+1

5. Isolate the variable terms by adding 5*t to both sides.

4=7*t+1

6. Isolate the constant terms by subtracting 1 from both sides.

3=7*t

7. Solve for t by dividing both sides by 7

t=3/7

Final Answer

(t−1)*(t−4)=(t+1)2⇒t=3/7

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