(2y-7)(2-y)=0

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


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

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

Multiply (-7 + 2y) * (2 + -1y)
(-7(2 + -1y) + 2y * (2 + -1y)) = 0
((2 * -7 + -1y * -7) + 2y * (2 + -1y)) = 0
((-14 + 7y) + 2y * (2 + -1y)) = 0
(-14 + 7y + (2 * 2y + -1y * 2y)) = 0
(-14 + 7y + (4y + -2y2)) = 0

Combine like terms: 7y + 4y = 11y
(-14 + 11y + -2y2) = 0

Solving
-14 + 11y + -2y2 = 0

Solving for variable 'y'.

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


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

Simplifying
-7 + 2y = 0

Solving
-7 + 2y = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2y = 0 + 7

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

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

Divide each side by '2'.
y = 3.5

Simplifying
y = 3.5

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

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

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

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

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

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