4(2x+1)=27+3x(2x-5)

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Solution for 4(2x+1)=27+3x(2x-5) equation: 


Simplifying
4(2x + 1) = 27 + 3x(2x + -5)

Reorder the terms:
4(1 + 2x) = 27 + 3x(2x + -5)
(1 * 4 + 2x * 4) = 27 + 3x(2x + -5)
(4 + 8x) = 27 + 3x(2x + -5)

Reorder the terms:
4 + 8x = 27 + 3x(-5 + 2x)
4 + 8x = 27 + (-5 * 3x + 2x * 3x)
4 + 8x = 27 + (-15x + 6x2)

Solving
4 + 8x = 27 + -15x + 6x2

Solving for variable 'x'.

Reorder the terms:
4 + -27 + 8x + 15x + -6x2 = 27 + -15x + 6x2 + -27 + 15x + -6x2

Combine like terms: 4 + -27 = -23
-23 + 8x + 15x + -6x2 = 27 + -15x + 6x2 + -27 + 15x + -6x2

Combine like terms: 8x + 15x = 23x
-23 + 23x + -6x2 = 27 + -15x + 6x2 + -27 + 15x + -6x2

Reorder the terms:
-23 + 23x + -6x2 = 27 + -27 + -15x + 15x + 6x2 + -6x2

Combine like terms: 27 + -27 = 0
-23 + 23x + -6x2 = 0 + -15x + 15x + 6x2 + -6x2
-23 + 23x + -6x2 = -15x + 15x + 6x2 + -6x2

Combine like terms: -15x + 15x = 0
-23 + 23x + -6x2 = 0 + 6x2 + -6x2
-23 + 23x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-23 + 23x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
3.833333333 + -3.833333333x + x2 = 0

Move the constant term to the right:

Add '-3.833333333' to each side of the equation.
3.833333333 + -3.833333333x + -3.833333333 + x2 = 0 + -3.833333333

Reorder the terms:
3.833333333 + -3.833333333 + -3.833333333x + x2 = 0 + -3.833333333

Combine like terms: 3.833333333 + -3.833333333 = 0.000000000
0.000000000 + -3.833333333x + x2 = 0 + -3.833333333
-3.833333333x + x2 = 0 + -3.833333333

Combine like terms: 0 + -3.833333333 = -3.833333333
-3.833333333x + x2 = -3.833333333

The x term is -3.833333333x.  Take half its coefficient (-1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
-3.833333333x + 3.673611112 + x2 = -3.833333333 + 3.673611112

Reorder the terms:
3.673611112 + -3.833333333x + x2 = -3.833333333 + 3.673611112

Combine like terms: -3.833333333 + 3.673611112 = -0.159722221
3.673611112 + -3.833333333x + x2 = -0.159722221

Factor a perfect square on the left side:
(x + -1.916666667)(x + -1.916666667) = -0.159722221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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