(x^2+bx+c)(ax^2+bx+c)=

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Solution for (x^2+bx+c)(ax^2+bx+c)= equation: 


Simplifying
(x2 + bx + c)(ax2 + bx + c) = 0

Reorder the terms:
(bx + c + x2)(ax2 + bx + c) = 0

Multiply (bx + c + x2) * (ax2 + bx + c)
(bx(ax2 + bx + c) + c(ax2 + bx + c) + x2(ax2 + bx + c)) = 0
((ax2 * bx + bx * bx + c * bx) + c(ax2 + bx + c) + x2(ax2 + bx + c)) = 0

Reorder the terms:
((abx3 + bcx + b2x2) + c(ax2 + bx + c) + x2(ax2 + bx + c)) = 0
((abx3 + bcx + b2x2) + c(ax2 + bx + c) + x2(ax2 + bx + c)) = 0
(abx3 + bcx + b2x2 + (ax2 * c + bx * c + c * c) + x2(ax2 + bx + c)) = 0
(abx3 + bcx + b2x2 + (acx2 + bcx + c2) + x2(ax2 + bx + c)) = 0
(abx3 + bcx + b2x2 + acx2 + bcx + c2 + (ax2 * x2 + bx * x2 + c * x2)) = 0
(abx3 + bcx + b2x2 + acx2 + bcx + c2 + (ax4 + bx3 + cx2)) = 0

Reorder the terms:
(abx3 + acx2 + ax4 + bcx + bcx + bx3 + b2x2 + cx2 + c2) = 0

Combine like terms: bcx + bcx = 2bcx
(abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2) = 0

Solving
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = 0

Solving for variable 'a'.

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

Add '-2bcx' to each side of the equation.
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + -2bcx + c2 = 0 + -2bcx

Reorder the terms:
abx3 + acx2 + ax4 + 2bcx + -2bcx + bx3 + b2x2 + cx2 + c2 = 0 + -2bcx

Combine like terms: 2bcx + -2bcx = 0
abx3 + acx2 + ax4 + 0 + bx3 + b2x2 + cx2 + c2 = 0 + -2bcx
abx3 + acx2 + ax4 + bx3 + b2x2 + cx2 + c2 = 0 + -2bcx
Remove the zero:
abx3 + acx2 + ax4 + bx3 + b2x2 + cx2 + c2 = -2bcx

Add '-1bx3' to each side of the equation.
abx3 + acx2 + ax4 + bx3 + b2x2 + cx2 + -1bx3 + c2 = -2bcx + -1bx3

Reorder the terms:
abx3 + acx2 + ax4 + bx3 + -1bx3 + b2x2 + cx2 + c2 = -2bcx + -1bx3

Combine like terms: bx3 + -1bx3 = 0
abx3 + acx2 + ax4 + 0 + b2x2 + cx2 + c2 = -2bcx + -1bx3
abx3 + acx2 + ax4 + b2x2 + cx2 + c2 = -2bcx + -1bx3

Add '-1b2x2' to each side of the equation.
abx3 + acx2 + ax4 + b2x2 + cx2 + -1b2x2 + c2 = -2bcx + -1bx3 + -1b2x2

Reorder the terms:
abx3 + acx2 + ax4 + b2x2 + -1b2x2 + cx2 + c2 = -2bcx + -1bx3 + -1b2x2

Combine like terms: b2x2 + -1b2x2 = 0
abx3 + acx2 + ax4 + 0 + cx2 + c2 = -2bcx + -1bx3 + -1b2x2
abx3 + acx2 + ax4 + cx2 + c2 = -2bcx + -1bx3 + -1b2x2

Add '-1cx2' to each side of the equation.
abx3 + acx2 + ax4 + cx2 + -1cx2 + c2 = -2bcx + -1bx3 + -1b2x2 + -1cx2

Combine like terms: cx2 + -1cx2 = 0
abx3 + acx2 + ax4 + 0 + c2 = -2bcx + -1bx3 + -1b2x2 + -1cx2
abx3 + acx2 + ax4 + c2 = -2bcx + -1bx3 + -1b2x2 + -1cx2

Add '-1c2' to each side of the equation.
abx3 + acx2 + ax4 + c2 + -1c2 = -2bcx + -1bx3 + -1b2x2 + -1cx2 + -1c2

Combine like terms: c2 + -1c2 = 0
abx3 + acx2 + ax4 + 0 = -2bcx + -1bx3 + -1b2x2 + -1cx2 + -1c2
abx3 + acx2 + ax4 = -2bcx + -1bx3 + -1b2x2 + -1cx2 + -1c2

Reorder the terms:
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = -2bcx + 2bcx + -1bx3 + bx3 + -1b2x2 + b2x2 + -1cx2 + cx2 + -1c2 + c2

Combine like terms: -2bcx + 2bcx = 0
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = 0 + -1bx3 + bx3 + -1b2x2 + b2x2 + -1cx2 + cx2 + -1c2 + c2
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = -1bx3 + bx3 + -1b2x2 + b2x2 + -1cx2 + cx2 + -1c2 + c2

Combine like terms: -1bx3 + bx3 = 0
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = 0 + -1b2x2 + b2x2 + -1cx2 + cx2 + -1c2 + c2
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = -1b2x2 + b2x2 + -1cx2 + cx2 + -1c2 + c2

Combine like terms: -1b2x2 + b2x2 = 0
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = 0 + -1cx2 + cx2 + -1c2 + c2
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = -1cx2 + cx2 + -1c2 + c2

Combine like terms: -1cx2 + cx2 = 0
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = 0 + -1c2 + c2
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = -1c2 + c2

Combine like terms: -1c2 + c2 = 0
abx3 + acx2 + ax4 + 2bcx + bx3 + b2x2 + cx2 + c2 = 0

The solution to this equation could not be determined.

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