(12-9x)(-4x+10)=0

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Solution for (12-9x)(-4x+10)=0 equation: 


Simplifying
(12 + -9x)(-4x + 10) = 0

Reorder the terms:
(12 + -9x)(10 + -4x) = 0

Multiply (12 + -9x) * (10 + -4x)
(12(10 + -4x) + -9x * (10 + -4x)) = 0
((10 * 12 + -4x * 12) + -9x * (10 + -4x)) = 0
((120 + -48x) + -9x * (10 + -4x)) = 0
(120 + -48x + (10 * -9x + -4x * -9x)) = 0
(120 + -48x + (-90x + 36x2)) = 0

Combine like terms: -48x + -90x = -138x
(120 + -138x + 36x2) = 0

Solving
120 + -138x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(20 + -23x + 6x2) = 0

Factor a trinomial.
6((4 + -3x)(5 + -2x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
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
Solution
x = {1.333333333, 2.5}

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