(2-3x)(3x-10)-3x-1(8)=0

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Solution for (2-3x)(3x-10)-3x-1(8)=0 equation: 


Simplifying
(2 + -3x)(3x + -10) + -3x + -1(8) = 0

Reorder the terms:
(2 + -3x)(-10 + 3x) + -3x + -1(8) = 0

Multiply (2 + -3x) * (-10 + 3x)
(2(-10 + 3x) + -3x * (-10 + 3x)) + -3x + -1(8) = 0
((-10 * 2 + 3x * 2) + -3x * (-10 + 3x)) + -3x + -1(8) = 0
((-20 + 6x) + -3x * (-10 + 3x)) + -3x + -1(8) = 0
(-20 + 6x + (-10 * -3x + 3x * -3x)) + -3x + -1(8) = 0
(-20 + 6x + (30x + -9x2)) + -3x + -1(8) = 0

Combine like terms: 6x + 30x = 36x
(-20 + 36x + -9x2) + -3x + -1(8) = 0

Multiply -1 * 8
-20 + 36x + -9x2 + -3x + -8 = 0

Reorder the terms:
-20 + -8 + 36x + -3x + -9x2 = 0

Combine like terms: -20 + -8 = -28
-28 + 36x + -3x + -9x2 = 0

Combine like terms: 36x + -3x = 33x
-28 + 33x + -9x2 = 0

Solving
-28 + 33x + -9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + 3x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-7 + 3x)' equal to zero and attempt to solve:

Simplifying
-7 + 3x = 0

Solving
-7 + 3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x = 0 + 7
3x = 0 + 7

Combine like terms: 0 + 7 = 7
3x = 7

Divide each side by '3'.
x = 2.333333333

Simplifying
x = 2.333333333

Subproblem 2
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
Solution
x = {2.333333333, 1.333333333}

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