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

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

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

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

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

Multiply (-2 + 4x) * (-3 + x)
(-2(-3 + x) + 4x * (-3 + x)) = 0
((-3 * -2 + x * -2) + 4x * (-3 + x)) = 0
((6 + -2x) + 4x * (-3 + x)) = 0
(6 + -2x + (-3 * 4x + x * 4x)) = 0
(6 + -2x + (-12x + 4x2)) = 0

Combine like terms: -2x + -12x = -14x
(6 + -14x + 4x2) = 0

Solving
6 + -14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -7x + 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}