(2x+3)(x-6)-2x+3x+30=

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Solution for (2x+3)(x-6)-2x+3x+30= equation: 


Simplifying
(2x + 3)(x + -6) + -2x + 3x + 30 = 0

Reorder the terms:
(3 + 2x)(x + -6) + -2x + 3x + 30 = 0

Reorder the terms:
(3 + 2x)(-6 + x) + -2x + 3x + 30 = 0

Multiply (3 + 2x) * (-6 + x)
(3(-6 + x) + 2x * (-6 + x)) + -2x + 3x + 30 = 0
((-6 * 3 + x * 3) + 2x * (-6 + x)) + -2x + 3x + 30 = 0
((-18 + 3x) + 2x * (-6 + x)) + -2x + 3x + 30 = 0
(-18 + 3x + (-6 * 2x + x * 2x)) + -2x + 3x + 30 = 0
(-18 + 3x + (-12x + 2x2)) + -2x + 3x + 30 = 0

Combine like terms: 3x + -12x = -9x
(-18 + -9x + 2x2) + -2x + 3x + 30 = 0

Reorder the terms:
-18 + 30 + -9x + -2x + 3x + 2x2 = 0

Combine like terms: -18 + 30 = 12
12 + -9x + -2x + 3x + 2x2 = 0

Combine like terms: -9x + -2x = -11x
12 + -11x + 3x + 2x2 = 0

Combine like terms: -11x + 3x = -8x
12 + -8x + 2x2 = 0

Solving
12 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -4x + x2 = 0

Solving
6 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -4x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -4x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -4x + x2 = 0 + -6
-4x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-4x + x2 = -6

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -6 + 4

Reorder the terms:
4 + -4x + x2 = -6 + 4

Combine like terms: -6 + 4 = -2
4 + -4x + x2 = -2

Factor a perfect square on the left side:
(x + -2)(x + -2) = -2

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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