6a^2-4[2b-4b(b+3)]=0

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Solution for 6a^2-4[2b-4b(b+3)]=0 equation: 


Simplifying
6a2 + -4[2b + -4b(b + 3)] = 0

Reorder the terms:
6a2 + -4[2b + -4b(3 + b)] = 0
6a2 + -4[2b + (3 * -4b + b * -4b)] = 0
6a2 + -4[2b + (-12b + -4b2)] = 0

Combine like terms: 2b + -12b = -10b
6a2 + -4[-10b + -4b2] = 0
6a2 + [-10b * -4 + -4b2 * -4] = 0
6a2 + [40b + 16b2] = 0

Solving
6a2 + 40b + 16b2 = 0

Solving for variable 'a'.

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

Add '-40b' to each side of the equation.
6a2 + 40b + -40b + 16b2 = 0 + -40b

Combine like terms: 40b + -40b = 0
6a2 + 0 + 16b2 = 0 + -40b
6a2 + 16b2 = 0 + -40b
Remove the zero:
6a2 + 16b2 = -40b

Add '-16b2' to each side of the equation.
6a2 + 16b2 + -16b2 = -40b + -16b2

Combine like terms: 16b2 + -16b2 = 0
6a2 + 0 = -40b + -16b2
6a2 = -40b + -16b2

Divide each side by '6'.
a2 = -6.666666667b + -2.666666667b2

Simplifying
a2 = -6.666666667b + -2.666666667b2

Reorder the terms:
a2 + 6.666666667b + 2.666666667b2 = -6.666666667b + 6.666666667b + -2.666666667b2 + 2.666666667b2

Combine like terms: -6.666666667b + 6.666666667b = 0.000000000
a2 + 6.666666667b + 2.666666667b2 = 0.000000000 + -2.666666667b2 + 2.666666667b2
a2 + 6.666666667b + 2.666666667b2 = -2.666666667b2 + 2.666666667b2

Combine like terms: -2.666666667b2 + 2.666666667b2 = 0.000000000
a2 + 6.666666667b + 2.666666667b2 = 0.000000000

The solution to this equation could not be determined.

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