((2)*(x-3))+((7x-2)*(3(x-1)))=

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Solution for ((2)*(x-3))+((7x-2)*(3(x-1)))= equation: 


Simplifying
((2)(x + -3)) + ((7x + -2)(3(x + -1))) = 0

Reorder the terms:
(2(-3 + x)) + ((7x + -2)(3(x + -1))) = 0
((-3 * 2 + x * 2)) + ((7x + -2)(3(x + -1))) = 0
((-6 + 2x)) + ((7x + -2)(3(x + -1))) = 0
(-6 + 2x) + ((7x + -2)(3(x + -1))) = 0

Remove parenthesis around (-6 + 2x)
-6 + 2x + ((7x + -2)(3(x + -1))) = 0

Reorder the terms:
-6 + 2x + ((-2 + 7x)(3(x + -1))) = 0

Reorder the terms:
-6 + 2x + ((-2 + 7x)(3(-1 + x))) = 0
-6 + 2x + ((-2 + 7x)((-1 * 3 + x * 3))) = 0
-6 + 2x + ((-2 + 7x)((-3 + 3x))) = 0

Multiply (-2 + 7x) * (-3 + 3x)
-6 + 2x + ((-2(-3 + 3x) + 7x * (-3 + 3x))) = 0
-6 + 2x + (((-3 * -2 + 3x * -2) + 7x * (-3 + 3x))) = 0
-6 + 2x + (((6 + -6x) + 7x * (-3 + 3x))) = 0
-6 + 2x + ((6 + -6x + (-3 * 7x + 3x * 7x))) = 0
-6 + 2x + ((6 + -6x + (-21x + 21x2))) = 0

Combine like terms: -6x + -21x = -27x
-6 + 2x + ((6 + -27x + 21x2)) = 0
-6 + 2x + (6 + -27x + 21x2) = 0

Remove parenthesis around (6 + -27x + 21x2)
-6 + 2x + 6 + -27x + 21x2 = 0

Reorder the terms:
-6 + 6 + 2x + -27x + 21x2 = 0

Combine like terms: -6 + 6 = 0
0 + 2x + -27x + 21x2 = 0
2x + -27x + 21x2 = 0

Combine like terms: 2x + -27x = -25x
-25x + 21x2 = 0

Solving
-25x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-25 + 21x) = 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 '(-25 + 21x)' equal to zero and attempt to solve:

Simplifying
-25 + 21x = 0

Solving
-25 + 21x = 0

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

Add '25' to each side of the equation.
-25 + 25 + 21x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 21x = 0 + 25
21x = 0 + 25

Combine like terms: 0 + 25 = 25
21x = 25

Divide each side by '21'.
x = 1.19047619

Simplifying
x = 1.19047619
Solution
x = {0, 1.19047619}

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