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

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Solution for (x-4)(x)+(2x-1)=x-(4-x) equation:


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

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

Reorder the terms for easier multiplication:
x(-4 + x) + (2x + -1) = x + -1(4 + -1x)
(-4 * x + x * x) + (2x + -1) = x + -1(4 + -1x)
(-4x + x2) + (2x + -1) = x + -1(4 + -1x)

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

Remove parenthesis around (-1 + 2x)
-4x + x2 + -1 + 2x = x + -1(4 + -1x)

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

Combine like terms: -4x + 2x = -2x
-1 + -2x + x2 = x + -1(4 + -1x)
-1 + -2x + x2 = x + (4 * -1 + -1x * -1)
-1 + -2x + x2 = x + (-4 + 1x)

Reorder the terms:
-1 + -2x + x2 = -4 + x + 1x

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

Solving
-1 + -2x + x2 = -4 + 2x

Solving for variable 'x'.

Reorder the terms:
-1 + 4 + -2x + -2x + x2 = -4 + 2x + 4 + -2x

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

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

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

Combine like terms: -4 + 4 = 0
3 + -4x + x2 = 0 + 2x + -2x
3 + -4x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
3 + -4x + x2 = 0

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

Subproblem 1

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

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 = {1, 3}

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