2x(4-x)=6

Solution for 2x(4-x)=6 equation:

Simplifying
2x(4 + -1x) = 6
(4 * 2x + -1x * 2x) = 6
(8x + -2x2) = 6

Solving
8x + -2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 8x + -2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4x + -1x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {3, 1}