(5x-1)(7-x)=0

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Solution for (5x-1)(7-x)=0 equation: 


Simplifying
(5x + -1)(7 + -1x) = 0

Reorder the terms:
(-1 + 5x)(7 + -1x) = 0

Multiply (-1 + 5x) * (7 + -1x)
(-1(7 + -1x) + 5x * (7 + -1x)) = 0
((7 * -1 + -1x * -1) + 5x * (7 + -1x)) = 0
((-7 + 1x) + 5x * (7 + -1x)) = 0
(-7 + 1x + (7 * 5x + -1x * 5x)) = 0
(-7 + 1x + (35x + -5x2)) = 0

Combine like terms: 1x + 35x = 36x
(-7 + 36x + -5x2) = 0

Solving
-7 + 36x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + x)(1 + -5x) = 0


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

Simplifying
-7 + x = 0

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

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

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

Simplifying
x = 7

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {7, 0.2}

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