2b+3(4c+2d)6(3b-2c)=

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Solution for 2b+3(4c+2d)6(3b-2c)= equation:


Simplifying
2b + 3(4c + 2d) * 6(3b + -2c) = 0

Reorder the terms for easier multiplication:
2b + 3 * 6(4c + 2d)(3b + -2c) = 0

Multiply 3 * 6
2b + 18(4c + 2d)(3b + -2c) = 0

Multiply (4c + 2d) * (3b + -2c)
2b + 18(4c * (3b + -2c) + 2d * (3b + -2c)) = 0
2b + 18((3b * 4c + -2c * 4c) + 2d * (3b + -2c)) = 0
2b + 18((12bc + -8c2) + 2d * (3b + -2c)) = 0
2b + 18(12bc + -8c2 + (3b * 2d + -2c * 2d)) = 0
2b + 18(12bc + -8c2 + (6bd + -4cd)) = 0

Reorder the terms:
2b + 18(12bc + 6bd + -4cd + -8c2) = 0
2b + 18(12bc + 6bd + -4cd + -8c2) = 0
2b + (12bc * 18 + 6bd * 18 + -4cd * 18 + -8c2 * 18) = 0
2b + (216bc + 108bd + -72cd + -144c2) = 0

Solving
2b + 216bc + 108bd + -72cd + -144c2 = 0

Solving for variable 'b'.

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

Add '72cd' to each side of the equation.
2b + 216bc + 108bd + -72cd + 72cd + -144c2 = 0 + 72cd

Combine like terms: -72cd + 72cd = 0
2b + 216bc + 108bd + 0 + -144c2 = 0 + 72cd
2b + 216bc + 108bd + -144c2 = 0 + 72cd
Remove the zero:
2b + 216bc + 108bd + -144c2 = 72cd

Add '144c2' to each side of the equation.
2b + 216bc + 108bd + -144c2 + 144c2 = 72cd + 144c2

Combine like terms: -144c2 + 144c2 = 0
2b + 216bc + 108bd + 0 = 72cd + 144c2
2b + 216bc + 108bd = 72cd + 144c2

Reorder the terms:
2b + 216bc + 108bd + -72cd + -144c2 = 72cd + -72cd + 144c2 + -144c2

Combine like terms: 72cd + -72cd = 0
2b + 216bc + 108bd + -72cd + -144c2 = 0 + 144c2 + -144c2
2b + 216bc + 108bd + -72cd + -144c2 = 144c2 + -144c2

Combine like terms: 144c2 + -144c2 = 0
2b + 216bc + 108bd + -72cd + -144c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(b + 108bc + 54bd + -36cd + -72c2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(b + 108bc + 54bd + -36cd + -72c2)' equal to zero and attempt to solve: Simplifying b + 108bc + 54bd + -36cd + -72c2 = 0 Solving b + 108bc + 54bd + -36cd + -72c2 = 0 Move all terms containing b to the left, all other terms to the right. Add '36cd' to each side of the equation. b + 108bc + 54bd + -36cd + 36cd + -72c2 = 0 + 36cd Combine like terms: -36cd + 36cd = 0 b + 108bc + 54bd + 0 + -72c2 = 0 + 36cd b + 108bc + 54bd + -72c2 = 0 + 36cd Remove the zero: b + 108bc + 54bd + -72c2 = 36cd Add '72c2' to each side of the equation. b + 108bc + 54bd + -72c2 + 72c2 = 36cd + 72c2 Combine like terms: -72c2 + 72c2 = 0 b + 108bc + 54bd + 0 = 36cd + 72c2 b + 108bc + 54bd = 36cd + 72c2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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