(3y-7)(4-y)=0

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Solution for (3y-7)(4-y)=0 equation:


Simplifying
(3y + -7)(4 + -1y) = 0

Reorder the terms:
(-7 + 3y)(4 + -1y) = 0

Multiply (-7 + 3y) * (4 + -1y)
(-7(4 + -1y) + 3y * (4 + -1y)) = 0
((4 * -7 + -1y * -7) + 3y * (4 + -1y)) = 0
((-28 + 7y) + 3y * (4 + -1y)) = 0
(-28 + 7y + (4 * 3y + -1y * 3y)) = 0
(-28 + 7y + (12y + -3y2)) = 0

Combine like terms: 7y + 12y = 19y
(-28 + 19y + -3y2) = 0

Solving
-28 + 19y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + y)(7 + -3y) = 0

Subproblem 1

Set the factor '(-4 + y)' equal to zero and attempt to solve: Simplifying -4 + y = 0 Solving -4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + y = 0 + 4 y = 0 + 4 Combine like terms: 0 + 4 = 4 y = 4 Simplifying y = 4

Subproblem 2

Set the factor '(7 + -3y)' equal to zero and attempt to solve: Simplifying 7 + -3y = 0 Solving 7 + -3y = 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 + -3y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3y = 0 + -7 -3y = 0 + -7 Combine like terms: 0 + -7 = -7 -3y = -7 Divide each side by '-3'. y = 2.333333333 Simplifying y = 2.333333333

Solution

y = {4, 2.333333333}

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