(sqrt(4x+3))(sqrt(9x-16))=0

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Solution for (sqrt(4x+3))(sqrt(9x-16))=0 equation: 


Simplifying
(sqrt(4x + 3))(sqrt(9x + -16)) = 0

Reorder the terms:
(qrst(3 + 4x))(sqrt(9x + -16)) = 0
((3 * qrst + 4x * qrst))(sqrt(9x + -16)) = 0
((3qrst + 4qrstx))(sqrt(9x + -16)) = 0

Reorder the terms:
(3qrst + 4qrstx)(qrst(-16 + 9x)) = 0
(3qrst + 4qrstx)((-16 * qrst + 9x * qrst)) = 0
(3qrst + 4qrstx)((-16qrst + 9qrstx)) = 0

Multiply (3qrst + 4qrstx) * (-16qrst + 9qrstx)
(3qrst * (-16qrst + 9qrstx) + 4qrstx * (-16qrst + 9qrstx)) = 0
((-16qrst * 3qrst + 9qrstx * 3qrst) + 4qrstx * (-16qrst + 9qrstx)) = 0
((-48q2r2s2t2 + 27q2r2s2t2x) + 4qrstx * (-16qrst + 9qrstx)) = 0
(-48q2r2s2t2 + 27q2r2s2t2x + (-16qrst * 4qrstx + 9qrstx * 4qrstx)) = 0
(-48q2r2s2t2 + 27q2r2s2t2x + (-64q2r2s2t2x + 36q2r2s2t2x2)) = 0

Combine like terms: 27q2r2s2t2x + -64q2r2s2t2x = -37q2r2s2t2x
(-48q2r2s2t2 + -37q2r2s2t2x + 36q2r2s2t2x2) = 0

Solving
-48q2r2s2t2 + -37q2r2s2t2x + 36q2r2s2t2x2 = 0

Solving for variable 'q'.

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

Factor out the Greatest Common Factor (GCF), 'q2r2s2t2'.
q2r2s2t2(-48 + -37x + 36x2) = 0

Factor a trinomial.
q2r2s2t2((-3 + -4x)(16 + -9x)) = 0


Subproblem 1
Set the factor 'q2r2s2t2' equal to zero and attempt to solve:

Simplifying
q2r2s2t2 = 0

Solving
q2r2s2t2 = 0

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

Simplifying
q2r2s2t2 = 0

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 '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Add '4x' to each side of the equation.
-4x + 4x = 3 + 4x

Combine like terms: -4x + 4x = 0
0 = 3 + 4x

Simplifying
0 = 3 + 4x

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(16 + -9x)' equal to zero and attempt to solve:

Simplifying
16 + -9x = 0

Solving
16 + -9x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -9x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -9x = 0 + -16
-9x = 0 + -16

Combine like terms: 0 + -16 = -16
-9x = -16

Add '9x' to each side of the equation.
-9x + 9x = -16 + 9x

Combine like terms: -9x + 9x = 0
0 = -16 + 9x

Simplifying
0 = -16 + 9x

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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