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

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


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

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

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

Multiply (2 + 4y) * (-7 + 2y)
(2(-7 + 2y) + 4y * (-7 + 2y)) = 0
((-7 * 2 + 2y * 2) + 4y * (-7 + 2y)) = 0
((-14 + 4y) + 4y * (-7 + 2y)) = 0
(-14 + 4y + (-7 * 4y + 2y * 4y)) = 0
(-14 + 4y + (-28y + 8y2)) = 0

Combine like terms: 4y + -28y = -24y
(-14 + -24y + 8y2) = 0

Solving
-14 + -24y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -12y + 4y2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 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 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {-0.5, 3.5}

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