4(y-7)(-y-3)=0

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Solution for 4(y-7)(-y-3)=0 equation: 


Simplifying
4(y + -7)(-1y + -3) = 0

Reorder the terms:
4(-7 + y)(-1y + -3) = 0

Reorder the terms:
4(-7 + y)(-3 + -1y) = 0

Multiply (-7 + y) * (-3 + -1y)
4(-7(-3 + -1y) + y(-3 + -1y)) = 0
4((-3 * -7 + -1y * -7) + y(-3 + -1y)) = 0
4((21 + 7y) + y(-3 + -1y)) = 0
4(21 + 7y + (-3 * y + -1y * y)) = 0
4(21 + 7y + (-3y + -1y2)) = 0

Combine like terms: 7y + -3y = 4y
4(21 + 4y + -1y2) = 0
(21 * 4 + 4y * 4 + -1y2 * 4) = 0
(84 + 16y + -4y2) = 0

Solving
84 + 16y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + 4y + -1y2) = 0

Factor a trinomial.
4((7 + -1y)(3 + y)) = 0

Ignore the factor 4.

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

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7

Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {7, -3}

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