4a(ax^2+bx+c)=4a(0)

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Solution for 4a(ax^2+bx+c)=4a(0) equation: 


Simplifying
4a(ax2 + bx + c) = 4a(0)
(ax2 * 4a + bx * 4a + c * 4a) = 4a(0)

Reorder the terms:
(4abx + 4ac + 4a2x2) = 4a(0)
(4abx + 4ac + 4a2x2) = 4a(0)

Reorder the terms for easier multiplication:
4abx + 4ac + 4a2x2 = 4 * 0a

Multiply 4 * 0
4abx + 4ac + 4a2x2 = 0a

Anything times zero is zero.
4abx + 4ac + 4a2x2 = 0a

Solving
4abx + 4ac + 4a2x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(bx + c + ax2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(bx + c + ax2)' equal to zero and attempt to solve:

Simplifying
bx + c + ax2 = 0

Reorder the terms:
ax2 + bx + c = 0

Solving
ax2 + bx + c = 0

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

Add '-1bx' to each side of the equation.
ax2 + bx + -1bx + c = 0 + -1bx

Combine like terms: bx + -1bx = 0
ax2 + 0 + c = 0 + -1bx
ax2 + c = 0 + -1bx
Remove the zero:
ax2 + c = -1bx

Add '-1c' to each side of the equation.
ax2 + c + -1c = -1bx + -1c

Combine like terms: c + -1c = 0
ax2 + 0 = -1bx + -1c
ax2 = -1bx + -1c

Divide each side by 'x2'.
a = -1bx-1 + -1cx-2

Simplifying
a = -1bx-1 + -1cx-2
Solution
a = {0, -1bx-1 + -1cx-2}

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