3(4x+3)(4x+3)=48x

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Solution for 3(4x+3)(4x+3)=48x equation: 


Simplifying
3(4x + 3)(4x + 3) = 48x

Reorder the terms:
3(3 + 4x)(4x + 3) = 48x

Reorder the terms:
3(3 + 4x)(3 + 4x) = 48x

Multiply (3 + 4x) * (3 + 4x)
3(3(3 + 4x) + 4x * (3 + 4x)) = 48x
3((3 * 3 + 4x * 3) + 4x * (3 + 4x)) = 48x
3((9 + 12x) + 4x * (3 + 4x)) = 48x
3(9 + 12x + (3 * 4x + 4x * 4x)) = 48x
3(9 + 12x + (12x + 16x2)) = 48x

Combine like terms: 12x + 12x = 24x
3(9 + 24x + 16x2) = 48x
(9 * 3 + 24x * 3 + 16x2 * 3) = 48x
(27 + 72x + 48x2) = 48x

Solving
27 + 72x + 48x2 = 48x

Solving for variable 'x'.

Reorder the terms:
27 + 72x + -48x + 48x2 = 48x + -48x

Combine like terms: 72x + -48x = 24x
27 + 24x + 48x2 = 48x + -48x

Combine like terms: 48x + -48x = 0
27 + 24x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 8x + 16x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + 8x + 16x2)' equal to zero and attempt to solve:

Simplifying
9 + 8x + 16x2 = 0

Solving
9 + 8x + 16x2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
0.5625 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.5625' to each side of the equation.
0.5625 + 0.5x + -0.5625 + x2 = 0 + -0.5625

Reorder the terms:
0.5625 + -0.5625 + 0.5x + x2 = 0 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + 0.5x + x2 = 0 + -0.5625
0.5x + x2 = 0 + -0.5625

Combine like terms: 0 + -0.5625 = -0.5625
0.5x + x2 = -0.5625

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.5625 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.5625 + 0.0625

Combine like terms: -0.5625 + 0.0625 = -0.5
0.0625 + 0.5x + x2 = -0.5

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -0.5

Can't calculate square root of the right side.

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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