(y+2)(1-13y)+(5y-3)(3+5y)-(2y+7)(6y-1)=-13

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Solution for (y+2)(1-13y)+(5y-3)(3+5y)-(2y+7)(6y-1)=-13 equation: 


Simplifying
(y + 2)(1 + -13y) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13

Reorder the terms:
(2 + y)(1 + -13y) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13

Multiply (2 + y) * (1 + -13y)
(2(1 + -13y) + y(1 + -13y)) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13
((1 * 2 + -13y * 2) + y(1 + -13y)) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13
((2 + -26y) + y(1 + -13y)) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13
(2 + -26y + (1 * y + -13y * y)) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13
(2 + -26y + (1y + -13y2)) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13

Combine like terms: -26y + 1y = -25y
(2 + -25y + -13y2) + (5y + -3)(3 + 5y) + -1(2y + 7)(6y + -1) = -13

Reorder the terms:
2 + -25y + -13y2 + (-3 + 5y)(3 + 5y) + -1(2y + 7)(6y + -1) = -13

Multiply (-3 + 5y) * (3 + 5y)
2 + -25y + -13y2 + (-3(3 + 5y) + 5y * (3 + 5y)) + -1(2y + 7)(6y + -1) = -13
2 + -25y + -13y2 + ((3 * -3 + 5y * -3) + 5y * (3 + 5y)) + -1(2y + 7)(6y + -1) = -13
2 + -25y + -13y2 + ((-9 + -15y) + 5y * (3 + 5y)) + -1(2y + 7)(6y + -1) = -13
2 + -25y + -13y2 + (-9 + -15y + (3 * 5y + 5y * 5y)) + -1(2y + 7)(6y + -1) = -13
2 + -25y + -13y2 + (-9 + -15y + (15y + 25y2)) + -1(2y + 7)(6y + -1) = -13

Combine like terms: -15y + 15y = 0
2 + -25y + -13y2 + (-9 + 0 + 25y2) + -1(2y + 7)(6y + -1) = -13
2 + -25y + -13y2 + (-9 + 25y2) + -1(2y + 7)(6y + -1) = -13

Reorder the terms:
2 + -25y + -13y2 + -9 + 25y2 + -1(7 + 2y)(6y + -1) = -13

Reorder the terms:
2 + -25y + -13y2 + -9 + 25y2 + -1(7 + 2y)(-1 + 6y) = -13

Multiply (7 + 2y) * (-1 + 6y)
2 + -25y + -13y2 + -9 + 25y2 + -1(7(-1 + 6y) + 2y * (-1 + 6y)) = -13
2 + -25y + -13y2 + -9 + 25y2 + -1((-1 * 7 + 6y * 7) + 2y * (-1 + 6y)) = -13
2 + -25y + -13y2 + -9 + 25y2 + -1((-7 + 42y) + 2y * (-1 + 6y)) = -13
2 + -25y + -13y2 + -9 + 25y2 + -1(-7 + 42y + (-1 * 2y + 6y * 2y)) = -13
2 + -25y + -13y2 + -9 + 25y2 + -1(-7 + 42y + (-2y + 12y2)) = -13

Combine like terms: 42y + -2y = 40y
2 + -25y + -13y2 + -9 + 25y2 + -1(-7 + 40y + 12y2) = -13
2 + -25y + -13y2 + -9 + 25y2 + (-7 * -1 + 40y * -1 + 12y2 * -1) = -13
2 + -25y + -13y2 + -9 + 25y2 + (7 + -40y + -12y2) = -13

Reorder the terms:
2 + -9 + 7 + -25y + -40y + -13y2 + 25y2 + -12y2 = -13

Combine like terms: 2 + -9 = -7
-7 + 7 + -25y + -40y + -13y2 + 25y2 + -12y2 = -13

Combine like terms: -7 + 7 = 0
0 + -25y + -40y + -13y2 + 25y2 + -12y2 = -13
-25y + -40y + -13y2 + 25y2 + -12y2 = -13

Combine like terms: -25y + -40y = -65y
-65y + -13y2 + 25y2 + -12y2 = -13

Combine like terms: -13y2 + 25y2 = 12y2
-65y + 12y2 + -12y2 = -13

Combine like terms: 12y2 + -12y2 = 0
-65y + 0 = -13
-65y = -13

Solving
-65y = -13

Solving for variable 'y'.

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

Divide each side by '-65'.
y = 0.2

Simplifying
y = 0.2

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