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

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


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

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

Multiply (-7 + 2x) * (2 + -1x)
(-7(2 + -1x) + 2x * (2 + -1x)) = 0
((2 * -7 + -1x * -7) + 2x * (2 + -1x)) = 0
((-14 + 7x) + 2x * (2 + -1x)) = 0
(-14 + 7x + (2 * 2x + -1x * 2x)) = 0
(-14 + 7x + (4x + -2x2)) = 0

Combine like terms: 7x + 4x = 11x
(-14 + 11x + -2x2) = 0

Solving
-14 + 11x + -2x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 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 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {3.5, 2}

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