3x(x-4)+2x(3x-5)=0

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Solution for 3x(x-4)+2x(3x-5)=0 equation: 


Simplifying
3x(x + -4) + 2x(3x + -5) = 0

Reorder the terms:
3x(-4 + x) + 2x(3x + -5) = 0
(-4 * 3x + x * 3x) + 2x(3x + -5) = 0
(-12x + 3x2) + 2x(3x + -5) = 0

Reorder the terms:
-12x + 3x2 + 2x(-5 + 3x) = 0
-12x + 3x2 + (-5 * 2x + 3x * 2x) = 0
-12x + 3x2 + (-10x + 6x2) = 0

Reorder the terms:
-12x + -10x + 3x2 + 6x2 = 0

Combine like terms: -12x + -10x = -22x
-22x + 3x2 + 6x2 = 0

Combine like terms: 3x2 + 6x2 = 9x2
-22x + 9x2 = 0

Solving
-22x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-22 + 9x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-22 + 9x)' equal to zero and attempt to solve:

Simplifying
-22 + 9x = 0

Solving
-22 + 9x = 0

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

Add '22' to each side of the equation.
-22 + 22 + 9x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 9x = 0 + 22
9x = 0 + 22

Combine like terms: 0 + 22 = 22
9x = 22

Divide each side by '9'.
x = 2.444444444

Simplifying
x = 2.444444444
Solution
x = {0, 2.444444444}

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