(a+6)(3a-7)=0

Solution for (a+6)(3a-7)=0 equation:

Simplifying
(a + 6)(3a + -7) = 0

Reorder the terms:
(6 + a)(3a + -7) = 0

Reorder the terms:
(6 + a)(-7 + 3a) = 0

Multiply (6 + a) * (-7 + 3a)
(6(-7 + 3a) + a(-7 + 3a)) = 0
((-7 * 6 + 3a * 6) + a(-7 + 3a)) = 0
((-42 + 18a) + a(-7 + 3a)) = 0
(-42 + 18a + (-7 * a + 3a * a)) = 0
(-42 + 18a + (-7a + 3a2)) = 0

Combine like terms: 18a + -7a = 11a
(-42 + 11a + 3a2) = 0

Solving
-42 + 11a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a)(7 + -3a) = 0

Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(7 + -3a)' equal to zero and attempt to solve:

Simplifying
7 + -3a = 0

Solving
7 + -3a = 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 + -3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a = 0 + -7
-3a = 0 + -7

Combine like terms: 0 + -7 = -7
-3a = -7

Divide each side by '-3'.
a = 2.333333333

Simplifying
a = 2.333333333
Solution
a = {-6, 2.333333333}