Question

solve using the zero principle of zero products
(9t +5)(4t -12)=0

Answer 1

t=-5/9,3

Answer 2

(9t+5)(4t-12)=0

If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0.
(9t+5)=0_(4t-12)=0

Set the first factor equal to 0 and solve.
(9t+5)=0

Remove the parentheses around the expression 9t+5.
9t+5=0

Since 5 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 5 from both sides.
9t=-5

Divide each term in the equation by 9.
(9t)/(9)=-(5)/(9)

Simplify the left-hand side of the equation by canceling the common factors.
t=-(5)/(9)

Set the next factor equal to 0 and solve.
(4t-12)=0

Factor out the GCF of 4 from each term in the polynomial.
(4(t)+4(-3))=0

Factor out the GCF of 4 from 4t-12.
(4(t-3))=0

Divide both sides of the equation by 4. Dividing 0 by any non-zero number is 0.
(t-3)=0

Set each of the factors of the left-hand side of the equation equal to 0.
t-3=0

Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
t=3

The final solution is all the values that make (9t+5)(4t-12)=0 true.
t=-(5)/(9),3