13-13x=(4x+3)(x-1)

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Solution for 13-13x=(4x+3)(x-1) equation: 


Simplifying
13 + -13x = (4x + 3)(x + -1)

Reorder the terms:
13 + -13x = (3 + 4x)(x + -1)

Reorder the terms:
13 + -13x = (3 + 4x)(-1 + x)

Multiply (3 + 4x) * (-1 + x)
13 + -13x = (3(-1 + x) + 4x * (-1 + x))
13 + -13x = ((-1 * 3 + x * 3) + 4x * (-1 + x))
13 + -13x = ((-3 + 3x) + 4x * (-1 + x))
13 + -13x = (-3 + 3x + (-1 * 4x + x * 4x))
13 + -13x = (-3 + 3x + (-4x + 4x2))

Combine like terms: 3x + -4x = -1x
13 + -13x = (-3 + -1x + 4x2)

Solving
13 + -13x = -3 + -1x + 4x2

Solving for variable 'x'.

Reorder the terms:
13 + 3 + -13x + x + -4x2 = -3 + -1x + 4x2 + 3 + x + -4x2

Combine like terms: 13 + 3 = 16
16 + -13x + x + -4x2 = -3 + -1x + 4x2 + 3 + x + -4x2

Combine like terms: -13x + x = -12x
16 + -12x + -4x2 = -3 + -1x + 4x2 + 3 + x + -4x2

Reorder the terms:
16 + -12x + -4x2 = -3 + 3 + -1x + x + 4x2 + -4x2

Combine like terms: -3 + 3 = 0
16 + -12x + -4x2 = 0 + -1x + x + 4x2 + -4x2
16 + -12x + -4x2 = -1x + x + 4x2 + -4x2

Combine like terms: -1x + x = 0
16 + -12x + -4x2 = 0 + 4x2 + -4x2
16 + -12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
16 + -12x + -4x2 = 0

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

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

Ignore the factor 4.

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

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {1, -4}

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