4(y-7)-16y(y-7)=0

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Solution for 4(y-7)-16y(y-7)=0 equation: 


Simplifying
4(y + -7) + -16y(y + -7) = 0

Reorder the terms:
4(-7 + y) + -16y(y + -7) = 0
(-7 * 4 + y * 4) + -16y(y + -7) = 0
(-28 + 4y) + -16y(y + -7) = 0

Reorder the terms:
-28 + 4y + -16y(-7 + y) = 0
-28 + 4y + (-7 * -16y + y * -16y) = 0
-28 + 4y + (112y + -16y2) = 0

Combine like terms: 4y + 112y = 116y
-28 + 116y + -16y2 = 0

Solving
-28 + 116y + -16y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 29y + -4y2) = 0

Factor a trinomial.
4((-7 + y)(1 + -4y)) = 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 '(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 = {7, 0.25}

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