(2x-6)(16x-32)=0

Solution for (2x-6)(16x-32)=0 equation:

Simplifying
(2x + -6)(16x + -32) = 0

Reorder the terms:
(-6 + 2x)(16x + -32) = 0

Reorder the terms:
(-6 + 2x)(-32 + 16x) = 0

Multiply (-6 + 2x) * (-32 + 16x)
(-6(-32 + 16x) + 2x * (-32 + 16x)) = 0
((-32 * -6 + 16x * -6) + 2x * (-32 + 16x)) = 0
((192 + -96x) + 2x * (-32 + 16x)) = 0
(192 + -96x + (-32 * 2x + 16x * 2x)) = 0
(192 + -96x + (-64x + 32x2)) = 0

Combine like terms: -96x + -64x = -160x
(192 + -160x + 32x2) = 0

Solving
192 + -160x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '32'.
32(6 + -5x + x2) = 0

Factor a trinomial.
32((2 + -1x)(3 + -1x)) = 0

Ignore the factor 32.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, 3}