4*(2x+1)*(3x-9)=0

Solution for 4*(2x+1)*(3x-9)=0 equation:

Simplifying
4(2x + 1)(3x + -9) = 0

Reorder the terms:
4(1 + 2x)(3x + -9) = 0

Reorder the terms:
4(1 + 2x)(-9 + 3x) = 0

Multiply (1 + 2x) * (-9 + 3x)
4(1(-9 + 3x) + 2x * (-9 + 3x)) = 0
4((-9 * 1 + 3x * 1) + 2x * (-9 + 3x)) = 0
4((-9 + 3x) + 2x * (-9 + 3x)) = 0
4(-9 + 3x + (-9 * 2x + 3x * 2x)) = 0
4(-9 + 3x + (-18x + 6x2)) = 0

Combine like terms: 3x + -18x = -15x
4(-9 + -15x + 6x2) = 0
(-9 * 4 + -15x * 4 + 6x2 * 4) = 0
(-36 + -60x + 24x2) = 0

Solving
-36 + -60x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + -5x + 2x2) = 0

Factor a trinomial.
12((-1 + -2x)(3 + -1x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}