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

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


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

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

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

Multiply (-5 + 2y) * (4 + 2y)
(-5(4 + 2y) + 2y * (4 + 2y)) = 0
((4 * -5 + 2y * -5) + 2y * (4 + 2y)) = 0
((-20 + -10y) + 2y * (4 + 2y)) = 0
(-20 + -10y + (4 * 2y + 2y * 2y)) = 0
(-20 + -10y + (8y + 4y2)) = 0

Combine like terms: -10y + 8y = -2y
(-20 + -2y + 4y2) = 0

Solving
-20 + -2y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -1y + 2y2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-2, 2.5}

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