(7a+3)(4a-12)=0

Solution for (7a+3)(4a-12)=0 equation:

Simplifying
(7a + 3)(4a + -12) = 0

Reorder the terms:
(3 + 7a)(4a + -12) = 0

Reorder the terms:
(3 + 7a)(-12 + 4a) = 0

Multiply (3 + 7a) * (-12 + 4a)
(3(-12 + 4a) + 7a * (-12 + 4a)) = 0
((-12 * 3 + 4a * 3) + 7a * (-12 + 4a)) = 0
((-36 + 12a) + 7a * (-12 + 4a)) = 0
(-36 + 12a + (-12 * 7a + 4a * 7a)) = 0
(-36 + 12a + (-84a + 28a2)) = 0

Combine like terms: 12a + -84a = -72a
(-36 + -72a + 28a2) = 0

Solving
-36 + -72a + 28a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -18a + 7a2) = 0

Factor a trinomial.
4((-3 + -7a)(3 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -7a)' equal to zero and attempt to solve:

Simplifying
-3 + -7a = 0

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

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

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

Divide each side by '-7'.
a = -0.4285714286

Simplifying
a = -0.4285714286
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 = {-0.4285714286, 3}