6(x+2)+x(2x-3)=1

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Solution for 6(x+2)+x(2x-3)=1 equation: 


Simplifying
6(x + 2) + x(2x + -3) = 1

Reorder the terms:
6(2 + x) + x(2x + -3) = 1
(2 * 6 + x * 6) + x(2x + -3) = 1
(12 + 6x) + x(2x + -3) = 1

Reorder the terms:
12 + 6x + x(-3 + 2x) = 1
12 + 6x + (-3 * x + 2x * x) = 1
12 + 6x + (-3x + 2x2) = 1

Combine like terms: 6x + -3x = 3x
12 + 3x + 2x2 = 1

Solving
12 + 3x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
12 + -1 + 3x + 2x2 = 1 + -1

Combine like terms: 12 + -1 = 11
11 + 3x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
11 + 3x + 2x2 = 0

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

Divide each side by '2'.
5.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 1.5x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 1.5x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 1.5x + x2 = 0 + -5.5
1.5x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
1.5x + x2 = -5.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -5.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -5.5 + 0.5625

Combine like terms: -5.5 + 0.5625 = -4.9375
0.5625 + 1.5x + x2 = -4.9375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -4.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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