14=-3x(2x+3)+7x

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Solution for 14=-3x(2x+3)+7x equation: 


Simplifying
14 = -3x(2x + 3) + 7x

Reorder the terms:
14 = -3x(3 + 2x) + 7x
14 = (3 * -3x + 2x * -3x) + 7x
14 = (-9x + -6x2) + 7x

Reorder the terms:
14 = -9x + 7x + -6x2

Combine like terms: -9x + 7x = -2x
14 = -2x + -6x2

Solving
14 = -2x + -6x2

Solving for variable 'x'.

Reorder the terms:
14 + 2x + 6x2 = -2x + 2x + -6x2 + 6x2

Combine like terms: -2x + 2x = 0
14 + 2x + 6x2 = 0 + -6x2 + 6x2
14 + 2x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
14 + 2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
7 + x + 3x2 = 0

Solving
7 + x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 0.3333333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 0.3333333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + -2.333333333
0.3333333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
0.3333333333x + x2 = -2.333333333

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.
0.3333333333x + 0.25 + x2 = -2.333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -2.333333333 + 0.25

Combine like terms: -2.333333333 + 0.25 = -2.083333333
0.25 + 0.3333333333x + x2 = -2.083333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.083333333

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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