2(x-3)-4x=15-x(x+6)

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Solution for 2(x-3)-4x=15-x(x+6) equation: 


Simplifying
2(x + -3) + -4x = 15 + -1x(x + 6)

Reorder the terms:
2(-3 + x) + -4x = 15 + -1x(x + 6)
(-3 * 2 + x * 2) + -4x = 15 + -1x(x + 6)
(-6 + 2x) + -4x = 15 + -1x(x + 6)

Combine like terms: 2x + -4x = -2x
-6 + -2x = 15 + -1x(x + 6)

Reorder the terms:
-6 + -2x = 15 + -1x(6 + x)
-6 + -2x = 15 + (6 * -1x + x * -1x)
-6 + -2x = 15 + (-6x + -1x2)

Solving
-6 + -2x = 15 + -6x + -1x2

Solving for variable 'x'.

Reorder the terms:
-6 + -15 + -2x + 6x + x2 = 15 + -6x + -1x2 + -15 + 6x + x2

Combine like terms: -6 + -15 = -21
-21 + -2x + 6x + x2 = 15 + -6x + -1x2 + -15 + 6x + x2

Combine like terms: -2x + 6x = 4x
-21 + 4x + x2 = 15 + -6x + -1x2 + -15 + 6x + x2

Reorder the terms:
-21 + 4x + x2 = 15 + -15 + -6x + 6x + -1x2 + x2

Combine like terms: 15 + -15 = 0
-21 + 4x + x2 = 0 + -6x + 6x + -1x2 + x2
-21 + 4x + x2 = -6x + 6x + -1x2 + x2

Combine like terms: -6x + 6x = 0
-21 + 4x + x2 = 0 + -1x2 + x2
-21 + 4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-21 + 4x + x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -1x) = 0


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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7, 3}

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