-5x+3(x-4)+6=-2x(x+3)

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Solution for -5x+3(x-4)+6=-2x(x+3) equation: 


Simplifying
-5x + 3(x + -4) + 6 = -2x(x + 3)

Reorder the terms:
-5x + 3(-4 + x) + 6 = -2x(x + 3)
-5x + (-4 * 3 + x * 3) + 6 = -2x(x + 3)
-5x + (-12 + 3x) + 6 = -2x(x + 3)

Reorder the terms:
-12 + 6 + -5x + 3x = -2x(x + 3)

Combine like terms: -12 + 6 = -6
-6 + -5x + 3x = -2x(x + 3)

Combine like terms: -5x + 3x = -2x
-6 + -2x = -2x(x + 3)

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

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

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
2((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {-3, 1}

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