(x+2)*(2x-3)+x-4=-6

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Solution for (x+2)*(2x-3)+x-4=-6 equation: 


Simplifying
(x + 2)(2x + -3) + x + -4 = -6

Reorder the terms:
(2 + x)(2x + -3) + x + -4 = -6

Reorder the terms:
(2 + x)(-3 + 2x) + x + -4 = -6

Multiply (2 + x) * (-3 + 2x)
(2(-3 + 2x) + x(-3 + 2x)) + x + -4 = -6
((-3 * 2 + 2x * 2) + x(-3 + 2x)) + x + -4 = -6
((-6 + 4x) + x(-3 + 2x)) + x + -4 = -6
(-6 + 4x + (-3 * x + 2x * x)) + x + -4 = -6
(-6 + 4x + (-3x + 2x2)) + x + -4 = -6

Combine like terms: 4x + -3x = 1x
(-6 + 1x + 2x2) + x + -4 = -6

Reorder the terms:
-6 + -4 + 1x + x + 2x2 = -6

Combine like terms: -6 + -4 = -10
-10 + 1x + x + 2x2 = -6

Combine like terms: 1x + x = 2x
-10 + 2x + 2x2 = -6

Solving
-10 + 2x + 2x2 = -6

Solving for variable 'x'.

Reorder the terms:
-10 + 6 + 2x + 2x2 = -6 + 6

Combine like terms: -10 + 6 = -4
-4 + 2x + 2x2 = -6 + 6

Combine like terms: -6 + 6 = 0
-4 + 2x + 2x2 = 0

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

Factor a trinomial.
2((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-2, 1}

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