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

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Solution for (1-x)(3x-7)=0 equation: 


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

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

Multiply (1 + -1x) * (-7 + 3x)
(1(-7 + 3x) + -1x * (-7 + 3x)) = 0
((-7 * 1 + 3x * 1) + -1x * (-7 + 3x)) = 0
((-7 + 3x) + -1x * (-7 + 3x)) = 0
(-7 + 3x + (-7 * -1x + 3x * -1x)) = 0
(-7 + 3x + (7x + -3x2)) = 0

Combine like terms: 3x + 7x = 10x
(-7 + 10x + -3x2) = 0

Solving
-7 + 10x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + 3x)(1 + -1x) = 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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {2.333333333, 1}

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