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 = -7x
13 + -13x = (3 + -7x + 4x2)

Solving
13 + -13x = 3 + -7x + 4x2

Solving for variable 'x'.

Reorder the terms:
13 + -3 + -13x + 7x + -4x2 = 3 + -7x + 4x2 + -3 + 7x + -4x2

Combine like terms: 13 + -3 = 10
10 + -13x + 7x + -4x2 = 3 + -7x + 4x2 + -3 + 7x + -4x2

Combine like terms: -13x + 7x = -6x
10 + -6x + -4x2 = 3 + -7x + 4x2 + -3 + 7x + -4x2

Reorder the terms:
10 + -6x + -4x2 = 3 + -3 + -7x + 7x + 4x2 + -4x2

Combine like terms: 3 + -3 = 0
10 + -6x + -4x2 = 0 + -7x + 7x + 4x2 + -4x2
10 + -6x + -4x2 = -7x + 7x + 4x2 + -4x2

Combine like terms: -7x + 7x = 0
10 + -6x + -4x2 = 0 + 4x2 + -4x2
10 + -6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
10 + -6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -3x + -2x2) = 0

Factor a trinomial.
2((1 + -1x)(5 + 2x)) = 0

Ignore the factor 2.

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {1, -2.5}

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