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

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

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

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

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

Multiply (-4 + x) * (3 + 2x)
2(-4(3 + 2x) + x(3 + 2x)) = 0
2((3 * -4 + 2x * -4) + x(3 + 2x)) = 0
2((-12 + -8x) + x(3 + 2x)) = 0
2(-12 + -8x + (3 * x + 2x * x)) = 0
2(-12 + -8x + (3x + 2x2)) = 0

Combine like terms: -8x + 3x = -5x
2(-12 + -5x + 2x2) = 0
(-12 * 2 + -5x * 2 + 2x2 * 2) = 0
(-24 + -10x + 4x2) = 0

Solving
-24 + -10x + 4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.5, 4}