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

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


Simplifying
(3y + -2)(7 + -1y) = 0

Reorder the terms:
(-2 + 3y)(7 + -1y) = 0

Multiply (-2 + 3y) * (7 + -1y)
(-2(7 + -1y) + 3y * (7 + -1y)) = 0
((7 * -2 + -1y * -2) + 3y * (7 + -1y)) = 0
((-14 + 2y) + 3y * (7 + -1y)) = 0
(-14 + 2y + (7 * 3y + -1y * 3y)) = 0
(-14 + 2y + (21y + -3y2)) = 0

Combine like terms: 2y + 21y = 23y
(-14 + 23y + -3y2) = 0

Solving
-14 + 23y + -3y2 = 0

Solving for variable 'y'.

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


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

Simplifying
-7 + y = 0

Solving
-7 + y = 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 + y = 0 + 7

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

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

Simplifying
y = 7

Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 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 + -3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y = 0 + -2
-3y = 0 + -2

Combine like terms: 0 + -2 = -2
-3y = -2

Divide each side by '-3'.
y = 0.6666666667

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

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