2x+4-6x+18=x^2+2x-3x-6

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Solution for 2x+4-6x+18=x^2+2x-3x-6 equation: 


Simplifying
2x + 4 + -6x + 18 = x2 + 2x + -3x + -6

Reorder the terms:
4 + 18 + 2x + -6x = x2 + 2x + -3x + -6

Combine like terms: 4 + 18 = 22
22 + 2x + -6x = x2 + 2x + -3x + -6

Combine like terms: 2x + -6x = -4x
22 + -4x = x2 + 2x + -3x + -6

Reorder the terms:
22 + -4x = -6 + 2x + -3x + x2

Combine like terms: 2x + -3x = -1x
22 + -4x = -6 + -1x + x2

Solving
22 + -4x = -6 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
22 + 6 + -4x + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: 22 + 6 = 28
28 + -4x + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: -4x + x = -3x
28 + -3x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Reorder the terms:
28 + -3x + -1x2 = -6 + 6 + -1x + x + x2 + -1x2

Combine like terms: -6 + 6 = 0
28 + -3x + -1x2 = 0 + -1x + x + x2 + -1x2
28 + -3x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
28 + -3x + -1x2 = 0 + x2 + -1x2
28 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + -3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(7 + x) = 0


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {4, -7}

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