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

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


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

Reorder the terms:
3y(-7 + y) + -4(y + -7) = 0
(-7 * 3y + y * 3y) + -4(y + -7) = 0
(-21y + 3y2) + -4(y + -7) = 0

Reorder the terms:
-21y + 3y2 + -4(-7 + y) = 0
-21y + 3y2 + (-7 * -4 + y * -4) = 0
-21y + 3y2 + (28 + -4y) = 0

Reorder the terms:
28 + -21y + -4y + 3y2 = 0

Combine like terms: -21y + -4y = -25y
28 + -25y + 3y2 = 0

Solving
28 + -25y + 3y2 = 0

Solving for variable 'y'.

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


Subproblem 1
Set the factor '(4 + -3y)' equal to zero and attempt to solve:

Simplifying
4 + -3y = 0

Solving
4 + -3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3y = 0 + -4
-3y = 0 + -4

Combine like terms: 0 + -4 = -4
-3y = -4

Divide each side by '-3'.
y = 1.333333333

Simplifying
y = 1.333333333

Subproblem 2
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
Solution
y = {1.333333333, 7}

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