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

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

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

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

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

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

Combine like terms: 6x + -1x = 5x
4(-3 + 5x + 2x2) = 0
(-3 * 4 + 5x * 4 + 2x2 * 4) = 0
(-12 + 20x + 8x2) = 0

Solving
-12 + 20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 5x + 2x2) = 0

Factor a trinomial.
4((-3 + -1x)(1 + -2x)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 0.5}