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

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

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

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

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

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

Combine like terms: -6x + 1x = -5x
2(-3 + -5x + 2x2) = 0
(-3 * 2 + -5x * 2 + 2x2 * 2) = 0
(-6 + -10x + 4x2) = 0

Solving
-6 + -10x + 4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
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}