12(5x+27)=4x(6-9x)

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Solution for 12(5x+27)=4x(6-9x) equation: 


Simplifying
12(5x + 27) = 4x(6 + -9x)

Reorder the terms:
12(27 + 5x) = 4x(6 + -9x)
(27 * 12 + 5x * 12) = 4x(6 + -9x)
(324 + 60x) = 4x(6 + -9x)
324 + 60x = (6 * 4x + -9x * 4x)
324 + 60x = (24x + -36x2)

Solving
324 + 60x = 24x + -36x2

Solving for variable 'x'.

Combine like terms: 60x + -24x = 36x
324 + 36x + 36x2 = 24x + -36x2 + -24x + 36x2

Reorder the terms:
324 + 36x + 36x2 = 24x + -24x + -36x2 + 36x2

Combine like terms: 24x + -24x = 0
324 + 36x + 36x2 = 0 + -36x2 + 36x2
324 + 36x + 36x2 = -36x2 + 36x2

Combine like terms: -36x2 + 36x2 = 0
324 + 36x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '36'.
36(9 + x + x2) = 0

Ignore the factor 36.

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

Simplifying
9 + x + x2 = 0

Solving
9 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x + x2 = 0 + -9
x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
x + x2 = -9

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

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -9 + 0.25

Reorder the terms:
0.25 + x + x2 = -9 + 0.25

Combine like terms: -9 + 0.25 = -8.75
0.25 + x + x2 = -8.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -8.75

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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