2(x-3)-3x(x-4)=10

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Solution for 2(x-3)-3x(x-4)=10 equation: 


Simplifying
2(x + -3) + -3x(x + -4) = 10

Reorder the terms:
2(-3 + x) + -3x(x + -4) = 10
(-3 * 2 + x * 2) + -3x(x + -4) = 10
(-6 + 2x) + -3x(x + -4) = 10

Reorder the terms:
-6 + 2x + -3x(-4 + x) = 10
-6 + 2x + (-4 * -3x + x * -3x) = 10
-6 + 2x + (12x + -3x2) = 10

Combine like terms: 2x + 12x = 14x
-6 + 14x + -3x2 = 10

Solving
-6 + 14x + -3x2 = 10

Solving for variable 'x'.

Reorder the terms:
-6 + -10 + 14x + -3x2 = 10 + -10

Combine like terms: -6 + -10 = -16
-16 + 14x + -3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-16 + 14x + -3x2 = 0

Factor a trinomial.
(-8 + 3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Divide each side by '3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
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
Solution
x = {2.666666667, 2}

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