(x-1)(5x+3)=(3x-8)(x-1)

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Solution for (x-1)(5x+3)=(3x-8)(x-1) equation: 


Simplifying
(x + -1)(5x + 3) = (3x + -8)(x + -1)

Reorder the terms:
(-1 + x)(5x + 3) = (3x + -8)(x + -1)

Reorder the terms:
(-1 + x)(3 + 5x) = (3x + -8)(x + -1)

Multiply (-1 + x) * (3 + 5x)
(-1(3 + 5x) + x(3 + 5x)) = (3x + -8)(x + -1)
((3 * -1 + 5x * -1) + x(3 + 5x)) = (3x + -8)(x + -1)
((-3 + -5x) + x(3 + 5x)) = (3x + -8)(x + -1)
(-3 + -5x + (3 * x + 5x * x)) = (3x + -8)(x + -1)
(-3 + -5x + (3x + 5x2)) = (3x + -8)(x + -1)

Combine like terms: -5x + 3x = -2x
(-3 + -2x + 5x2) = (3x + -8)(x + -1)

Reorder the terms:
-3 + -2x + 5x2 = (-8 + 3x)(x + -1)

Reorder the terms:
-3 + -2x + 5x2 = (-8 + 3x)(-1 + x)

Multiply (-8 + 3x) * (-1 + x)
-3 + -2x + 5x2 = (-8(-1 + x) + 3x * (-1 + x))
-3 + -2x + 5x2 = ((-1 * -8 + x * -8) + 3x * (-1 + x))
-3 + -2x + 5x2 = ((8 + -8x) + 3x * (-1 + x))
-3 + -2x + 5x2 = (8 + -8x + (-1 * 3x + x * 3x))
-3 + -2x + 5x2 = (8 + -8x + (-3x + 3x2))

Combine like terms: -8x + -3x = -11x
-3 + -2x + 5x2 = (8 + -11x + 3x2)

Solving
-3 + -2x + 5x2 = 8 + -11x + 3x2

Solving for variable 'x'.

Reorder the terms:
-3 + -8 + -2x + 11x + 5x2 + -3x2 = 8 + -11x + 3x2 + -8 + 11x + -3x2

Combine like terms: -3 + -8 = -11
-11 + -2x + 11x + 5x2 + -3x2 = 8 + -11x + 3x2 + -8 + 11x + -3x2

Combine like terms: -2x + 11x = 9x
-11 + 9x + 5x2 + -3x2 = 8 + -11x + 3x2 + -8 + 11x + -3x2

Combine like terms: 5x2 + -3x2 = 2x2
-11 + 9x + 2x2 = 8 + -11x + 3x2 + -8 + 11x + -3x2

Reorder the terms:
-11 + 9x + 2x2 = 8 + -8 + -11x + 11x + 3x2 + -3x2

Combine like terms: 8 + -8 = 0
-11 + 9x + 2x2 = 0 + -11x + 11x + 3x2 + -3x2
-11 + 9x + 2x2 = -11x + 11x + 3x2 + -3x2

Combine like terms: -11x + 11x = 0
-11 + 9x + 2x2 = 0 + 3x2 + -3x2
-11 + 9x + 2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-11 + 9x + 2x2 = 0

Factor a trinomial.
(-11 + -2x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -2x)' equal to zero and attempt to solve:

Simplifying
-11 + -2x = 0

Solving
-11 + -2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x = 0 + 11
-2x = 0 + 11

Combine like terms: 0 + 11 = 11
-2x = 11

Divide each side by '-2'.
x = -5.5

Simplifying
x = -5.5

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 = {-5.5, 1}

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