x(x-1)=(x+6)(1-x)

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Solution for x(x-1)=(x+6)(1-x) equation:


Simplifying
x(x + -1) = (x + 6)(1 + -1x)

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

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

Multiply (6 + x) * (1 + -1x)
-1x + x2 = (6(1 + -1x) + x(1 + -1x))
-1x + x2 = ((1 * 6 + -1x * 6) + x(1 + -1x))
-1x + x2 = ((6 + -6x) + x(1 + -1x))
-1x + x2 = (6 + -6x + (1 * x + -1x * x))
-1x + x2 = (6 + -6x + (1x + -1x2))

Combine like terms: -6x + 1x = -5x
-1x + x2 = (6 + -5x + -1x2)

Solving
-1x + x2 = 6 + -5x + -1x2

Solving for variable 'x'.

Reorder the terms:
-6 + -1x + 5x + x2 + x2 = 6 + -5x + -1x2 + -6 + 5x + x2

Combine like terms: -1x + 5x = 4x
-6 + 4x + x2 + x2 = 6 + -5x + -1x2 + -6 + 5x + x2

Combine like terms: x2 + x2 = 2x2
-6 + 4x + 2x2 = 6 + -5x + -1x2 + -6 + 5x + x2

Reorder the terms:
-6 + 4x + 2x2 = 6 + -6 + -5x + 5x + -1x2 + x2

Combine like terms: 6 + -6 = 0
-6 + 4x + 2x2 = 0 + -5x + 5x + -1x2 + x2
-6 + 4x + 2x2 = -5x + 5x + -1x2 + x2

Combine like terms: -5x + 5x = 0
-6 + 4x + 2x2 = 0 + -1x2 + x2
-6 + 4x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 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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