(6-4x)*(5-2x)=6

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Solution for (6-4x)*(5-2x)=6 equation: 


Simplifying
(6 + -4x)(5 + -2x) = 6

Multiply (6 + -4x) * (5 + -2x)
(6(5 + -2x) + -4x * (5 + -2x)) = 6
((5 * 6 + -2x * 6) + -4x * (5 + -2x)) = 6
((30 + -12x) + -4x * (5 + -2x)) = 6
(30 + -12x + (5 * -4x + -2x * -4x)) = 6
(30 + -12x + (-20x + 8x2)) = 6

Combine like terms: -12x + -20x = -32x
(30 + -32x + 8x2) = 6

Solving
30 + -32x + 8x2 = 6

Solving for variable 'x'.

Reorder the terms:
30 + -6 + -32x + 8x2 = 6 + -6

Combine like terms: 30 + -6 = 24
24 + -32x + 8x2 = 6 + -6

Combine like terms: 6 + -6 = 0
24 + -32x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(3 + -4x + x2) = 0

Factor a trinomial.
8((1 + -1x)(3 + -1x)) = 0

Ignore the factor 8.

Subproblem 1
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

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 = {1, 3}

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