(x+4)(9x-3)=0

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

Simplifying
(x + 4)(9x + -3) = 0

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

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

Multiply (4 + x) * (-3 + 9x)
(4(-3 + 9x) + x(-3 + 9x)) = 0
((-3 * 4 + 9x * 4) + x(-3 + 9x)) = 0
((-12 + 36x) + x(-3 + 9x)) = 0
(-12 + 36x + (-3 * x + 9x * x)) = 0
(-12 + 36x + (-3x + 9x2)) = 0

Combine like terms: 36x + -3x = 33x
(-12 + 33x + 9x2) = 0

Solving
-12 + 33x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 11x + 3x2) = 0

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

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-4, 0.3333333333}