(7a+4)(3a-9)=0

Solution for (7a+4)(3a-9)=0 equation:

Simplifying
(7a + 4)(3a + -9) = 0

Reorder the terms:
(4 + 7a)(3a + -9) = 0

Reorder the terms:
(4 + 7a)(-9 + 3a) = 0

Multiply (4 + 7a) * (-9 + 3a)
(4(-9 + 3a) + 7a * (-9 + 3a)) = 0
((-9 * 4 + 3a * 4) + 7a * (-9 + 3a)) = 0
((-36 + 12a) + 7a * (-9 + 3a)) = 0
(-36 + 12a + (-9 * 7a + 3a * 7a)) = 0
(-36 + 12a + (-63a + 21a2)) = 0

Combine like terms: 12a + -63a = -51a
(-36 + -51a + 21a2) = 0

Solving
-36 + -51a + 21a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -17a + 7a2) = 0

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

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

Simplifying
-4 + -7a = 0

Solving
-4 + -7a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7a = 0 + 4

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

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

Divide each side by '-7'.
a = -0.5714285714

Simplifying
a = -0.5714285714
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 = {-0.5714285714, 3}