(a+6)(4a-7)=0

Solution for (a+6)(4a-7)=0 equation:

Simplifying
(a + 6)(4a + -7) = 0

Reorder the terms:
(6 + a)(4a + -7) = 0

Reorder the terms:
(6 + a)(-7 + 4a) = 0

Multiply (6 + a) * (-7 + 4a)
(6(-7 + 4a) + a(-7 + 4a)) = 0
((-7 * 6 + 4a * 6) + a(-7 + 4a)) = 0
((-42 + 24a) + a(-7 + 4a)) = 0
(-42 + 24a + (-7 * a + 4a * a)) = 0
(-42 + 24a + (-7a + 4a2)) = 0

Combine like terms: 24a + -7a = 17a
(-42 + 17a + 4a2) = 0

Solving
-42 + 17a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a)(7 + -4a) = 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 + -4a)' equal to zero and attempt to solve:

Simplifying
7 + -4a = 0

Solving
7 + -4a = 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 + -4a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4a = 0 + -7
-4a = 0 + -7

Combine like terms: 0 + -7 = -7
-4a = -7

Divide each side by '-4'.
a = 1.75

Simplifying
a = 1.75
Solution
a = {-6, 1.75}