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

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


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

Reorder the terms:
-5x(-2 + x) + x = -1(x + -4)
(-2 * -5x + x * -5x) + x = -1(x + -4)
(10x + -5x2) + x = -1(x + -4)

Reorder the terms:
10x + x + -5x2 = -1(x + -4)

Combine like terms: 10x + x = 11x
11x + -5x2 = -1(x + -4)

Reorder the terms:
11x + -5x2 = -1(-4 + x)
11x + -5x2 = (-4 * -1 + x * -1)
11x + -5x2 = (4 + -1x)

Solving
11x + -5x2 = 4 + -1x

Solving for variable 'x'.

Reorder the terms:
-4 + 11x + x + -5x2 = 4 + -1x + -4 + x

Combine like terms: 11x + x = 12x
-4 + 12x + -5x2 = 4 + -1x + -4 + x

Reorder the terms:
-4 + 12x + -5x2 = 4 + -4 + -1x + x

Combine like terms: 4 + -4 = 0
-4 + 12x + -5x2 = 0 + -1x + x
-4 + 12x + -5x2 = -1x + x

Combine like terms: -1x + x = 0
-4 + 12x + -5x2 = 0

Factor a trinomial.
(-2 + x)(2 + -5x) = 0


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 '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {2, 0.4}

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