(-a^2+4d+3)(3d^2-7d+6)=

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Solution for (-a^2+4d+3)(3d^2-7d+6)= equation:


Simplifying
(-1a2 + 4d + 3)(3d2 + -7d + 6) = 0

Reorder the terms:
(3 + -1a2 + 4d)(3d2 + -7d + 6) = 0

Reorder the terms:
(3 + -1a2 + 4d)(6 + -7d + 3d2) = 0

Multiply (3 + -1a2 + 4d) * (6 + -7d + 3d2)
(3(6 + -7d + 3d2) + -1a2 * (6 + -7d + 3d2) + 4d * (6 + -7d + 3d2)) = 0
((6 * 3 + -7d * 3 + 3d2 * 3) + -1a2 * (6 + -7d + 3d2) + 4d * (6 + -7d + 3d2)) = 0
((18 + -21d + 9d2) + -1a2 * (6 + -7d + 3d2) + 4d * (6 + -7d + 3d2)) = 0
(18 + -21d + 9d2 + (6 * -1a2 + -7d * -1a2 + 3d2 * -1a2) + 4d * (6 + -7d + 3d2)) = 0
(18 + -21d + 9d2 + (-6a2 + 7a2d + -3a2d2) + 4d * (6 + -7d + 3d2)) = 0
(18 + -21d + 9d2 + -6a2 + 7a2d + -3a2d2 + (6 * 4d + -7d * 4d + 3d2 * 4d)) = 0
(18 + -21d + 9d2 + -6a2 + 7a2d + -3a2d2 + (24d + -28d2 + 12d3)) = 0

Reorder the terms:
(18 + -6a2 + 7a2d + -3a2d2 + -21d + 24d + 9d2 + -28d2 + 12d3) = 0

Combine like terms: -21d + 24d = 3d
(18 + -6a2 + 7a2d + -3a2d2 + 3d + 9d2 + -28d2 + 12d3) = 0

Combine like terms: 9d2 + -28d2 = -19d2
(18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3) = 0

Solving
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0

Solving for variable 'a'.

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

Add '-18' to each side of the equation.
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + -18 + 12d3 = 0 + -18

Reorder the terms:
18 + -18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0 + -18
-6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0 + -18

Combine like terms: 0 + -18 = -18
-6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = -18

Add '-3d' to each side of the equation.
-6a2 + 7a2d + -3a2d2 + 3d + -19d2 + -3d + 12d3 = -18 + -3d

Reorder the terms:
-6a2 + 7a2d + -3a2d2 + 3d + -3d + -19d2 + 12d3 = -18 + -3d

Combine like terms: 3d + -3d = 0
-6a2 + 7a2d + -3a2d2 + 0 + -19d2 + 12d3 = -18 + -3d
-6a2 + 7a2d + -3a2d2 + -19d2 + 12d3 = -18 + -3d

Add '19d2' to each side of the equation.
-6a2 + 7a2d + -3a2d2 + -19d2 + 19d2 + 12d3 = -18 + -3d + 19d2

Combine like terms: -19d2 + 19d2 = 0
-6a2 + 7a2d + -3a2d2 + 0 + 12d3 = -18 + -3d + 19d2
-6a2 + 7a2d + -3a2d2 + 12d3 = -18 + -3d + 19d2

Add '-12d3' to each side of the equation.
-6a2 + 7a2d + -3a2d2 + 12d3 + -12d3 = -18 + -3d + 19d2 + -12d3

Combine like terms: 12d3 + -12d3 = 0
-6a2 + 7a2d + -3a2d2 + 0 = -18 + -3d + 19d2 + -12d3
-6a2 + 7a2d + -3a2d2 = -18 + -3d + 19d2 + -12d3

Reorder the terms:
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = -18 + -3d + 19d2 + -12d3 + 18 + 3d + -19d2 + 12d3

Reorder the terms:
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = -18 + 18 + -3d + 3d + 19d2 + -19d2 + -12d3 + 12d3

Combine like terms: -18 + 18 = 0
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0 + -3d + 3d + 19d2 + -19d2 + -12d3 + 12d3
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = -3d + 3d + 19d2 + -19d2 + -12d3 + 12d3

Combine like terms: -3d + 3d = 0
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0 + 19d2 + -19d2 + -12d3 + 12d3
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 19d2 + -19d2 + -12d3 + 12d3

Combine like terms: 19d2 + -19d2 = 0
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0 + -12d3 + 12d3
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = -12d3 + 12d3

Combine like terms: -12d3 + 12d3 = 0
18 + -6a2 + 7a2d + -3a2d2 + 3d + -19d2 + 12d3 = 0

The solution to this equation could not be determined.

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