3(2x+1)(x-3)=0

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

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

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

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

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

Combine like terms: 1x + -6x = -5x
3(-3 + -5x + 2x2) = 0
(-3 * 3 + -5x * 3 + 2x2 * 3) = 0
(-9 + -15x + 6x2) = 0

Solving
-9 + -15x + 6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.
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}