(2x-6)(-3x+2)-8x+24=0

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Solution for (2x-6)(-3x+2)-8x+24=0 equation: 


Simplifying
(2x + -6)(-3x + 2) + -8x + 24 = 0

Reorder the terms:
(-6 + 2x)(-3x + 2) + -8x + 24 = 0

Reorder the terms:
(-6 + 2x)(2 + -3x) + -8x + 24 = 0

Multiply (-6 + 2x) * (2 + -3x)
(-6(2 + -3x) + 2x * (2 + -3x)) + -8x + 24 = 0
((2 * -6 + -3x * -6) + 2x * (2 + -3x)) + -8x + 24 = 0
((-12 + 18x) + 2x * (2 + -3x)) + -8x + 24 = 0
(-12 + 18x + (2 * 2x + -3x * 2x)) + -8x + 24 = 0
(-12 + 18x + (4x + -6x2)) + -8x + 24 = 0

Combine like terms: 18x + 4x = 22x
(-12 + 22x + -6x2) + -8x + 24 = 0

Reorder the terms:
-12 + 24 + 22x + -8x + -6x2 = 0

Combine like terms: -12 + 24 = 12
12 + 22x + -8x + -6x2 = 0

Combine like terms: 22x + -8x = 14x
12 + 14x + -6x2 = 0

Solving
12 + 14x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 7x + -3x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {3, -0.6666666667}

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