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

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


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

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

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

Multiply (-5 + 4y) * (2 + 4y)
0 = (-5(2 + 4y) + 4y * (2 + 4y))
0 = ((2 * -5 + 4y * -5) + 4y * (2 + 4y))
0 = ((-10 + -20y) + 4y * (2 + 4y))
0 = (-10 + -20y + (2 * 4y + 4y * 4y))
0 = (-10 + -20y + (8y + 16y2))

Combine like terms: -20y + 8y = -12y
0 = (-10 + -12y + 16y2)

Solving
0 = -10 + -12y + 16y2

Solving for variable 'y'.

Combine like terms: 0 + 10 = 10
10 + 12y + -16y2 = -10 + -12y + 16y2 + 10 + 12y + -16y2

Reorder the terms:
10 + 12y + -16y2 = -10 + 10 + -12y + 12y + 16y2 + -16y2

Combine like terms: -10 + 10 = 0
10 + 12y + -16y2 = 0 + -12y + 12y + 16y2 + -16y2
10 + 12y + -16y2 = -12y + 12y + 16y2 + -16y2

Combine like terms: -12y + 12y = 0
10 + 12y + -16y2 = 0 + 16y2 + -16y2
10 + 12y + -16y2 = 16y2 + -16y2

Combine like terms: 16y2 + -16y2 = 0
10 + 12y + -16y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 6y + -8y2) = 0

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

Ignore the factor 2.

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 '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

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

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

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {1.25, -0.5}

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