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

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

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

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

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

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

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

Solving
-9 + 3x + 6x2 = 0

Solving for variable 'x'.

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

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

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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.5, 1}