13*(4*y+6)*(2*y-7)=

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Solution for 13*(4*y+6)*(2*y-7)= equation: 


Simplifying
13(4y + 6)(2y + -7) = 0

Reorder the terms:
13(6 + 4y)(2y + -7) = 0

Reorder the terms:
13(6 + 4y)(-7 + 2y) = 0

Multiply (6 + 4y) * (-7 + 2y)
13(6(-7 + 2y) + 4y * (-7 + 2y)) = 0
13((-7 * 6 + 2y * 6) + 4y * (-7 + 2y)) = 0
13((-42 + 12y) + 4y * (-7 + 2y)) = 0
13(-42 + 12y + (-7 * 4y + 2y * 4y)) = 0
13(-42 + 12y + (-28y + 8y2)) = 0

Combine like terms: 12y + -28y = -16y
13(-42 + -16y + 8y2) = 0
(-42 * 13 + -16y * 13 + 8y2 * 13) = 0
(-546 + -208y + 104y2) = 0

Solving
-546 + -208y + 104y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '26'.
26(-21 + -8y + 4y2) = 0

Factor a trinomial.
26((-3 + -2y)(7 + -2y)) = 0

Ignore the factor 26.

Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve:

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y = 0 + 3
-2y = 0 + 3

Combine like terms: 0 + 3 = 3
-2y = 3

Divide each side by '-2'.
y = -1.5

Simplifying
y = -1.5

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

Simplifying
7 + -2y = 0

Solving
7 + -2y = 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 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {-1.5, 3.5}

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