x(3x-2)-7(3x-2)=0

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Solution for x(3x-2)-7(3x-2)=0 equation: 


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

Reorder the terms:
x(-2 + 3x) + -7(3x + -2) = 0
(-2 * x + 3x * x) + -7(3x + -2) = 0
(-2x + 3x2) + -7(3x + -2) = 0

Reorder the terms:
-2x + 3x2 + -7(-2 + 3x) = 0
-2x + 3x2 + (-2 * -7 + 3x * -7) = 0
-2x + 3x2 + (14 + -21x) = 0

Reorder the terms:
14 + -2x + -21x + 3x2 = 0

Combine like terms: -2x + -21x = -23x
14 + -23x + 3x2 = 0

Solving
14 + -23x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -3x)(7 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0.6666666667, 7}

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