Solve by factoring: 9t2 + 3t= 0

p2 + p + 4 = 0

To solve the equations by factoring, we need to factorize the expressions on the left-hand side of the equations.

1. Solve the equation 9t^2 + 3t = 0:
To factorize this equation, first, notice that both terms on the left side have a common factor of t.
We can factor out t to get: t(9t + 3) = 0

Now, we have two factors: t and (9t + 3).
To find the values of t that satisfy the equation, set each factor equal to zero and solve for t:
t = 0 (from the factor t = 0)
9t + 3 = 0 (from the factor 9t + 3 = 0)

Solving 9t + 3 = 0:
Subtract 3 from both sides: 9t = -3
Divide both sides by 9: t = -3/9
Simplifying the fraction: t = -1/3

So, the solutions to the equation 9t^2 + 3t = 0 are t = 0 and t = -1/3.

2. Solve the equation p^2 + p + 4 = 0:
This equation is in quadratic form.

To factorize this equation, we need to find two numbers whose product is equal to the product of the coefficient of p^2 (1) and the constant term (4), and whose sum is equal to the coefficient of p (1).

We need to find two numbers that satisfy the conditions. In this case, since the constant term is positive, and the coefficient of p is also positive, it is not possible to find two numbers that satisfy the conditions for factorization.

Therefore, we cannot solve the equation p^2 + p + 4 = 0 by factoring.

To find the solutions to this equation, we can use the quadratic formula or complete the square method.