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

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


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

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

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

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

Combine like terms: -7y + -4y = -11y
(28 + -11y + y2) = 0

Solving
28 + -11y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + -1y)(7 + -1y) = 0

Subproblem 1

Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 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 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4

Subproblem 2

Set the factor '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 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 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7

Solution

y = {4, 7}

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