4(y-5)(-y+7)=0

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Solution for 4(y-5)(-y+7)=0 equation: 


Simplifying
4(y + -5)(-1y + 7) = 0

Reorder the terms:
4(-5 + y)(-1y + 7) = 0

Reorder the terms:
4(-5 + y)(7 + -1y) = 0

Multiply (-5 + y) * (7 + -1y)
4(-5(7 + -1y) + y(7 + -1y)) = 0
4((7 * -5 + -1y * -5) + y(7 + -1y)) = 0
4((-35 + 5y) + y(7 + -1y)) = 0
4(-35 + 5y + (7 * y + -1y * y)) = 0
4(-35 + 5y + (7y + -1y2)) = 0

Combine like terms: 5y + 7y = 12y
4(-35 + 12y + -1y2) = 0
(-35 * 4 + 12y * 4 + -1y2 * 4) = 0
(-140 + 48y + -4y2) = 0

Solving
-140 + 48y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + 12y + -1y2) = 0

Factor a trinomial.
4((-7 + y)(5 + -1y)) = 0

Ignore the factor 4.

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

Simplifying
-7 + y = 0

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

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

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

Simplifying
y = 7

Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {7, 5}

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