(2x-3)(x+1)=2-(3x-1)(x+1)

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Solution for (2x-3)(x+1)=2-(3x-1)(x+1) equation:


Simplifying
(2x + -3)(x + 1) = 2 + -1(3x + -1)(x + 1)

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

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

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

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

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

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

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

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

Combine like terms: 2 + 1 = 3
-3 + -1x + 2x2 = 3 + -2x + -3x2

Solving
-3 + -1x + 2x2 = 3 + -2x + -3x2

Solving for variable 'x'.

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

Combine like terms: -3 + -3 = -6
-6 + -1x + 2x + 2x2 + 3x2 = 3 + -2x + -3x2 + -3 + 2x + 3x2

Combine like terms: -1x + 2x = 1x
-6 + 1x + 2x2 + 3x2 = 3 + -2x + -3x2 + -3 + 2x + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
-6 + 1x + 5x2 = 3 + -2x + -3x2 + -3 + 2x + 3x2

Reorder the terms:
-6 + 1x + 5x2 = 3 + -3 + -2x + 2x + -3x2 + 3x2

Combine like terms: 3 + -3 = 0
-6 + 1x + 5x2 = 0 + -2x + 2x + -3x2 + 3x2
-6 + 1x + 5x2 = -2x + 2x + -3x2 + 3x2

Combine like terms: -2x + 2x = 0
-6 + 1x + 5x2 = 0 + -3x2 + 3x2
-6 + 1x + 5x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-6 + 1x + 5x2 = 0

Factor a trinomial.
(-6 + -5x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2

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 = {-1.2, 1}

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