(2x-5)(3x-12)=0

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Solution for (2x-5)(3x-12)=0 equation: 


Simplifying
(2x + -5)(3x + -12) = 0

Reorder the terms:
(-5 + 2x)(3x + -12) = 0

Reorder the terms:
(-5 + 2x)(-12 + 3x) = 0

Multiply (-5 + 2x) * (-12 + 3x)
(-5(-12 + 3x) + 2x * (-12 + 3x)) = 0
((-12 * -5 + 3x * -5) + 2x * (-12 + 3x)) = 0
((60 + -15x) + 2x * (-12 + 3x)) = 0
(60 + -15x + (-12 * 2x + 3x * 2x)) = 0
(60 + -15x + (-24x + 6x2)) = 0

Combine like terms: -15x + -24x = -39x
(60 + -39x + 6x2) = 0

Solving
60 + -39x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -13x + 2x2) = 0

Factor a trinomial.
3((5 + -2x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2.5, 4}

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