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

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

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

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

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

Multiply (7 + 9a) * (-6 + 2a)
(7(-6 + 2a) + 9a * (-6 + 2a)) = 0
((-6 * 7 + 2a * 7) + 9a * (-6 + 2a)) = 0
((-42 + 14a) + 9a * (-6 + 2a)) = 0
(-42 + 14a + (-6 * 9a + 2a * 9a)) = 0
(-42 + 14a + (-54a + 18a2)) = 0

Combine like terms: 14a + -54a = -40a
(-42 + -40a + 18a2) = 0

Solving
-42 + -40a + 18a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -20a + 9a2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -9a)' equal to zero and attempt to solve:

Simplifying
-7 + -9a = 0

Solving
-7 + -9a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -9a = 0 + 7

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

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

Divide each side by '-9'.
a = -0.7777777778

Simplifying
a = -0.7777777778
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

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

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

Divide each side by '-1'.
a = 3

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