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

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


Simplifying
-4x(x + -2) + 5x = 2(x + 4) + -1x

Reorder the terms:
-4x(-2 + x) + 5x = 2(x + 4) + -1x
(-2 * -4x + x * -4x) + 5x = 2(x + 4) + -1x
(8x + -4x2) + 5x = 2(x + 4) + -1x

Reorder the terms:
8x + 5x + -4x2 = 2(x + 4) + -1x

Combine like terms: 8x + 5x = 13x
13x + -4x2 = 2(x + 4) + -1x

Reorder the terms:
13x + -4x2 = 2(4 + x) + -1x
13x + -4x2 = (4 * 2 + x * 2) + -1x
13x + -4x2 = (8 + 2x) + -1x

Combine like terms: 2x + -1x = 1x
13x + -4x2 = 8 + 1x

Solving
13x + -4x2 = 8 + 1x

Solving for variable 'x'.

Reorder the terms:
-8 + 13x + -1x + -4x2 = 8 + 1x + -8 + -1x

Combine like terms: 13x + -1x = 12x
-8 + 12x + -4x2 = 8 + 1x + -8 + -1x

Reorder the terms:
-8 + 12x + -4x2 = 8 + -8 + 1x + -1x

Combine like terms: 8 + -8 = 0
-8 + 12x + -4x2 = 0 + 1x + -1x
-8 + 12x + -4x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
-8 + 12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 3x + -1x2) = 0

Factor a trinomial.
4((-2 + x)(1 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

Combine like terms: 0 + 2 = 2
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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