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

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


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

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

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

Multiply (-3 + y) * (7 + 2y)
(-3(7 + 2y) + y(7 + 2y)) = 0
((7 * -3 + 2y * -3) + y(7 + 2y)) = 0
((-21 + -6y) + y(7 + 2y)) = 0
(-21 + -6y + (7 * y + 2y * y)) = 0
(-21 + -6y + (7y + 2y2)) = 0

Combine like terms: -6y + 7y = 1y
(-21 + 1y + 2y2) = 0

Solving
-21 + 1y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -2y)(3 + -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 '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3

Solution

y = {-3.5, 3}

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