(4y-7)(6-y)=0

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Solution for (4y-7)(6-y)=0 equation:


Simplifying
(4y + -7)(6 + -1y) = 0

Reorder the terms:
(-7 + 4y)(6 + -1y) = 0

Multiply (-7 + 4y) * (6 + -1y)
(-7(6 + -1y) + 4y * (6 + -1y)) = 0
((6 * -7 + -1y * -7) + 4y * (6 + -1y)) = 0
((-42 + 7y) + 4y * (6 + -1y)) = 0
(-42 + 7y + (6 * 4y + -1y * 4y)) = 0
(-42 + 7y + (24y + -4y2)) = 0

Combine like terms: 7y + 24y = 31y
(-42 + 31y + -4y2) = 0

Solving
-42 + 31y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + y)(7 + -4y) = 0

Subproblem 1

Set the factor '(-6 + y)' equal to zero and attempt to solve: Simplifying -6 + y = 0 Solving -6 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 0 + 6 Combine like terms: -6 + 6 = 0 0 + y = 0 + 6 y = 0 + 6 Combine like terms: 0 + 6 = 6 y = 6 Simplifying y = 6

Subproblem 2

Set the factor '(7 + -4y)' equal to zero and attempt to solve: Simplifying 7 + -4y = 0 Solving 7 + -4y = 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 + -4y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4y = 0 + -7 -4y = 0 + -7 Combine like terms: 0 + -7 = -7 -4y = -7 Divide each side by '-4'. y = 1.75 Simplifying y = 1.75

Solution

y = {6, 1.75}

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