5y(6y-7)(4y+7)=0

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Solution for 5y(6y-7)(4y+7)=0 equation: 


Simplifying
5y(6y + -7)(4y + 7) = 0

Reorder the terms:
5y(-7 + 6y)(4y + 7) = 0

Reorder the terms:
5y(-7 + 6y)(7 + 4y) = 0

Multiply (-7 + 6y) * (7 + 4y)
5y(-7(7 + 4y) + 6y * (7 + 4y)) = 0
5y((7 * -7 + 4y * -7) + 6y * (7 + 4y)) = 0
5y((-49 + -28y) + 6y * (7 + 4y)) = 0
5y(-49 + -28y + (7 * 6y + 4y * 6y)) = 0
5y(-49 + -28y + (42y + 24y2)) = 0

Combine like terms: -28y + 42y = 14y
5y(-49 + 14y + 24y2) = 0
(-49 * 5y + 14y * 5y + 24y2 * 5y) = 0
(-245y + 70y2 + 120y3) = 0

Solving
-245y + 70y2 + 120y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(-49 + 14y + 24y2) = 0

Factor a trinomial.
5y((-7 + -4y)(7 + -6y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(-7 + -4y)' equal to zero and attempt to solve:

Simplifying
-7 + -4y = 0

Solving
-7 + -4y = 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 + -4y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4y = 0 + 7
-4y = 0 + 7

Combine like terms: 0 + 7 = 7
-4y = 7

Divide each side by '-4'.
y = -1.75

Simplifying
y = -1.75

Subproblem 3
Set the factor '(7 + -6y)' equal to zero and attempt to solve:

Simplifying
7 + -6y = 0

Solving
7 + -6y = 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 + -6y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6y = 0 + -7
-6y = 0 + -7

Combine like terms: 0 + -7 = -7
-6y = -7

Divide each side by '-6'.
y = 1.166666667

Simplifying
y = 1.166666667
Solution
y = {0, -1.75, 1.166666667}

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