9y^2-42y+45=0

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Solution for 9y^2-42y+45=0 equation:


Simplifying
9y2 + -42y + 45 = 0

Reorder the terms:
45 + -42y + 9y2 = 0

Solving
45 + -42y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -14y + 3y2) = 0

Factor a trinomial.
3((5 + -3y)(3 + -1y)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -3y)' equal to zero and attempt to solve: Simplifying 5 + -3y = 0 Solving 5 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3y = 0 + -5 -3y = 0 + -5 Combine like terms: 0 + -5 = -5 -3y = -5 Divide each side by '-3'. y = 1.666666667 Simplifying y = 1.666666667

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 = {1.666666667, 3}

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