5-5x=(3x+4)(x-1)

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Solution for 5-5x=(3x+4)(x-1) equation: 


Simplifying
5 + -5x = (3x + 4)(x + -1)

Reorder the terms:
5 + -5x = (4 + 3x)(x + -1)

Reorder the terms:
5 + -5x = (4 + 3x)(-1 + x)

Multiply (4 + 3x) * (-1 + x)
5 + -5x = (4(-1 + x) + 3x * (-1 + x))
5 + -5x = ((-1 * 4 + x * 4) + 3x * (-1 + x))
5 + -5x = ((-4 + 4x) + 3x * (-1 + x))
5 + -5x = (-4 + 4x + (-1 * 3x + x * 3x))
5 + -5x = (-4 + 4x + (-3x + 3x2))

Combine like terms: 4x + -3x = 1x
5 + -5x = (-4 + 1x + 3x2)

Solving
5 + -5x = -4 + 1x + 3x2

Solving for variable 'x'.

Reorder the terms:
5 + 4 + -5x + -1x + -3x2 = -4 + 1x + 3x2 + 4 + -1x + -3x2

Combine like terms: 5 + 4 = 9
9 + -5x + -1x + -3x2 = -4 + 1x + 3x2 + 4 + -1x + -3x2

Combine like terms: -5x + -1x = -6x
9 + -6x + -3x2 = -4 + 1x + 3x2 + 4 + -1x + -3x2

Reorder the terms:
9 + -6x + -3x2 = -4 + 4 + 1x + -1x + 3x2 + -3x2

Combine like terms: -4 + 4 = 0
9 + -6x + -3x2 = 0 + 1x + -1x + 3x2 + -3x2
9 + -6x + -3x2 = 1x + -1x + 3x2 + -3x2

Combine like terms: 1x + -1x = 0
9 + -6x + -3x2 = 0 + 3x2 + -3x2
9 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
9 + -6x + -3x2 = 0

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

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

Ignore the factor 3.

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 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {1, -3}

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