(-4y-7)(-8y+2)=0

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Solution for (-4y-7)(-8y+2)=0 equation: 


Simplifying
(-4y + -7)(-8y + 2) = 0

Reorder the terms:
(-7 + -4y)(-8y + 2) = 0

Reorder the terms:
(-7 + -4y)(2 + -8y) = 0

Multiply (-7 + -4y) * (2 + -8y)
(-7(2 + -8y) + -4y * (2 + -8y)) = 0
((2 * -7 + -8y * -7) + -4y * (2 + -8y)) = 0
((-14 + 56y) + -4y * (2 + -8y)) = 0
(-14 + 56y + (2 * -4y + -8y * -4y)) = 0
(-14 + 56y + (-8y + 32y2)) = 0

Combine like terms: 56y + -8y = 48y
(-14 + 48y + 32y2) = 0

Solving
-14 + 48y + 32y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 24y + 16y2) = 0

Factor a trinomial.
2((-7 + -4y)(1 + -4y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -4y)' equal to zero and attempt to solve:

Simplifying
-7 + -4y = 0

Solving
-7 + -4y = 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 + -4y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4y = 0 + 7
-4y = 0 + 7

Combine like terms: 0 + 7 = 7
-4y = 7

Divide each side by '-4'.
y = -1.75

Simplifying
y = -1.75

Subproblem 2
Set the factor '(1 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 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 + -4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4y = 0 + -1
-4y = 0 + -1

Combine like terms: 0 + -1 = -1
-4y = -1

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
Solution
y = {-1.75, 0.25}

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