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

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


Simplifying
4(y + -7)(-1y + 2) = 0

Reorder the terms:
4(-7 + y)(-1y + 2) = 0

Reorder the terms:
4(-7 + y)(2 + -1y) = 0

Multiply (-7 + y) * (2 + -1y)
4(-7(2 + -1y) + y(2 + -1y)) = 0
4((2 * -7 + -1y * -7) + y(2 + -1y)) = 0
4((-14 + 7y) + y(2 + -1y)) = 0
4(-14 + 7y + (2 * y + -1y * y)) = 0
4(-14 + 7y + (2y + -1y2)) = 0

Combine like terms: 7y + 2y = 9y
4(-14 + 9y + -1y2) = 0
(-14 * 4 + 9y * 4 + -1y2 * 4) = 0
(-56 + 36y + -4y2) = 0

Solving
-56 + 36y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 9y + -1y2) = 0

Factor a trinomial.
4((-7 + y)(2 + -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 '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

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

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {7, 2}

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