(9t+7)(2t-6)=0

Solution for (9t+7)(2t-6)=0 equation:

Simplifying
(9t + 7)(2t + -6) = 0

Reorder the terms:
(7 + 9t)(2t + -6) = 0

Reorder the terms:
(7 + 9t)(-6 + 2t) = 0

Multiply (7 + 9t) * (-6 + 2t)
(7(-6 + 2t) + 9t * (-6 + 2t)) = 0
((-6 * 7 + 2t * 7) + 9t * (-6 + 2t)) = 0
((-42 + 14t) + 9t * (-6 + 2t)) = 0
(-42 + 14t + (-6 * 9t + 2t * 9t)) = 0
(-42 + 14t + (-54t + 18t2)) = 0

Combine like terms: 14t + -54t = -40t
(-42 + -40t + 18t2) = 0

Solving
-42 + -40t + 18t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -20t + 9t2) = 0

Factor a trinomial.
2((-7 + -9t)(3 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -9t)' equal to zero and attempt to solve:

Simplifying
-7 + -9t = 0

Solving
-7 + -9t = 0

Move all terms containing t to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -9t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -9t = 0 + 7
-9t = 0 + 7

Combine like terms: 0 + 7 = 7
-9t = 7

Divide each side by '-9'.
t = -0.7777777778

Simplifying
t = -0.7777777778
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-0.7777777778, 3}