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

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


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

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

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

Multiply (-5 + x) * (-3 + 4x)
(-5(-3 + 4x) + x(-3 + 4x)) = (1 + -3x)(x + 1)
((-3 * -5 + 4x * -5) + x(-3 + 4x)) = (1 + -3x)(x + 1)
((15 + -20x) + x(-3 + 4x)) = (1 + -3x)(x + 1)
(15 + -20x + (-3 * x + 4x * x)) = (1 + -3x)(x + 1)
(15 + -20x + (-3x + 4x2)) = (1 + -3x)(x + 1)

Combine like terms: -20x + -3x = -23x
(15 + -23x + 4x2) = (1 + -3x)(x + 1)

Reorder the terms:
15 + -23x + 4x2 = (1 + -3x)(1 + x)

Multiply (1 + -3x) * (1 + x)
15 + -23x + 4x2 = (1(1 + x) + -3x * (1 + x))
15 + -23x + 4x2 = ((1 * 1 + x * 1) + -3x * (1 + x))
15 + -23x + 4x2 = ((1 + 1x) + -3x * (1 + x))
15 + -23x + 4x2 = (1 + 1x + (1 * -3x + x * -3x))
15 + -23x + 4x2 = (1 + 1x + (-3x + -3x2))

Combine like terms: 1x + -3x = -2x
15 + -23x + 4x2 = (1 + -2x + -3x2)

Solving
15 + -23x + 4x2 = 1 + -2x + -3x2

Solving for variable 'x'.

Reorder the terms:
15 + -1 + -23x + 2x + 4x2 + 3x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2

Combine like terms: 15 + -1 = 14
14 + -23x + 2x + 4x2 + 3x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2

Combine like terms: -23x + 2x = -21x
14 + -21x + 4x2 + 3x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2

Combine like terms: 4x2 + 3x2 = 7x2
14 + -21x + 7x2 = 1 + -2x + -3x2 + -1 + 2x + 3x2

Reorder the terms:
14 + -21x + 7x2 = 1 + -1 + -2x + 2x + -3x2 + 3x2

Combine like terms: 1 + -1 = 0
14 + -21x + 7x2 = 0 + -2x + 2x + -3x2 + 3x2
14 + -21x + 7x2 = -2x + 2x + -3x2 + 3x2

Combine like terms: -2x + 2x = 0
14 + -21x + 7x2 = 0 + -3x2 + 3x2
14 + -21x + 7x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
14 + -21x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(2 + -3x + x2) = 0

Factor a trinomial.
7((1 + -1x)(2 + -1x)) = 0

Ignore the factor 7.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}

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