(4x-12)(5x-10)=0

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Solution for (4x-12)(5x-10)=0 equation: 


Simplifying
(4x + -12)(5x + -10) = 0

Reorder the terms:
(-12 + 4x)(5x + -10) = 0

Reorder the terms:
(-12 + 4x)(-10 + 5x) = 0

Multiply (-12 + 4x) * (-10 + 5x)
(-12(-10 + 5x) + 4x * (-10 + 5x)) = 0
((-10 * -12 + 5x * -12) + 4x * (-10 + 5x)) = 0
((120 + -60x) + 4x * (-10 + 5x)) = 0
(120 + -60x + (-10 * 4x + 5x * 4x)) = 0
(120 + -60x + (-40x + 20x2)) = 0

Combine like terms: -60x + -40x = -100x
(120 + -100x + 20x2) = 0

Solving
120 + -100x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(6 + -5x + x2) = 0

Factor a trinomial.
20((2 + -1x)(3 + -1x)) = 0

Ignore the factor 20.

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}

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