(4y+5)(y-2)=0

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Solution for (4y+5)(y-2)=0 equation: 


Simplifying
(4y + 5)(y + -2) = 0

Reorder the terms:
(5 + 4y)(y + -2) = 0

Reorder the terms:
(5 + 4y)(-2 + y) = 0

Multiply (5 + 4y) * (-2 + y)
(5(-2 + y) + 4y * (-2 + y)) = 0
((-2 * 5 + y * 5) + 4y * (-2 + y)) = 0
((-10 + 5y) + 4y * (-2 + y)) = 0
(-10 + 5y + (-2 * 4y + y * 4y)) = 0
(-10 + 5y + (-8y + 4y2)) = 0

Combine like terms: 5y + -8y = -3y
(-10 + -3y + 4y2) = 0

Solving
-10 + -3y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + -4y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-5 + -4y)' equal to zero and attempt to solve:

Simplifying
-5 + -4y = 0

Solving
-5 + -4y = 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 + -4y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4y = 0 + 5
-4y = 0 + 5

Combine like terms: 0 + 5 = 5
-4y = 5

Divide each side by '-4'.
y = -1.25

Simplifying
y = -1.25

Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-1.25, 2}

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