(2ax+bx)(2ax+bx)=

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Solution for (2ax+bx)(2ax+bx)= equation: 


Simplifying
(2ax + bx)(2ax + bx) = 0

Multiply (2ax + bx) * (2ax + bx)
(2ax * (2ax + bx) + bx(2ax + bx)) = 0
((2ax * 2ax + bx * 2ax) + bx(2ax + bx)) = 0

Reorder the terms:
((2abx2 + 4a2x2) + bx(2ax + bx)) = 0
((2abx2 + 4a2x2) + bx(2ax + bx)) = 0
(2abx2 + 4a2x2 + (2ax * bx + bx * bx)) = 0
(2abx2 + 4a2x2 + (2abx2 + b2x2)) = 0

Reorder the terms:
(2abx2 + 2abx2 + 4a2x2 + b2x2) = 0

Combine like terms: 2abx2 + 2abx2 = 4abx2
(4abx2 + 4a2x2 + b2x2) = 0

Solving
4abx2 + 4a2x2 + b2x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4ab + 4a2 + b2) = 0

Factor a trinomial.
x2((2a + b)(2a + b)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 = 0 + -1x2
Remove the zero:
0 = -1x2

Simplifying
0 = -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2a + b)' equal to zero and attempt to solve:

Simplifying
2a + b = 0

Solving
2a + b = 0

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

Add '-1b' to each side of the equation.
2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
2a + 0 = 0 + -1b
2a = 0 + -1b
Remove the zero:
2a = -1b

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b

Subproblem 3
Set the factor '(2a + b)' equal to zero and attempt to solve:

Simplifying
2a + b = 0

Solving
2a + b = 0

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

Add '-1b' to each side of the equation.
2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
2a + 0 = 0 + -1b
2a = 0 + -1b
Remove the zero:
2a = -1b

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b
Solution
a = {-0.5b, -0.5b}

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