(2x-3)(x+1)-(x+1)(4x+2)=0

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Solution for (2x-3)(x+1)-(x+1)(4x+2)=0 equation:


Simplifying
(2x + -3)(x + 1) + -1(x + 1)(4x + 2) = 0

Reorder the terms:
(-3 + 2x)(x + 1) + -1(x + 1)(4x + 2) = 0

Reorder the terms:
(-3 + 2x)(1 + x) + -1(x + 1)(4x + 2) = 0

Multiply (-3 + 2x) * (1 + x)
(-3(1 + x) + 2x * (1 + x)) + -1(x + 1)(4x + 2) = 0
((1 * -3 + x * -3) + 2x * (1 + x)) + -1(x + 1)(4x + 2) = 0
((-3 + -3x) + 2x * (1 + x)) + -1(x + 1)(4x + 2) = 0
(-3 + -3x + (1 * 2x + x * 2x)) + -1(x + 1)(4x + 2) = 0
(-3 + -3x + (2x + 2x2)) + -1(x + 1)(4x + 2) = 0

Combine like terms: -3x + 2x = -1x
(-3 + -1x + 2x2) + -1(x + 1)(4x + 2) = 0

Reorder the terms:
-3 + -1x + 2x2 + -1(1 + x)(4x + 2) = 0

Reorder the terms:
-3 + -1x + 2x2 + -1(1 + x)(2 + 4x) = 0

Multiply (1 + x) * (2 + 4x)
-3 + -1x + 2x2 + -1(1(2 + 4x) + x(2 + 4x)) = 0
-3 + -1x + 2x2 + -1((2 * 1 + 4x * 1) + x(2 + 4x)) = 0
-3 + -1x + 2x2 + -1((2 + 4x) + x(2 + 4x)) = 0
-3 + -1x + 2x2 + -1(2 + 4x + (2 * x + 4x * x)) = 0
-3 + -1x + 2x2 + -1(2 + 4x + (2x + 4x2)) = 0

Combine like terms: 4x + 2x = 6x
-3 + -1x + 2x2 + -1(2 + 6x + 4x2) = 0
-3 + -1x + 2x2 + (2 * -1 + 6x * -1 + 4x2 * -1) = 0
-3 + -1x + 2x2 + (-2 + -6x + -4x2) = 0

Reorder the terms:
-3 + -2 + -1x + -6x + 2x2 + -4x2 = 0

Combine like terms: -3 + -2 = -5
-5 + -1x + -6x + 2x2 + -4x2 = 0

Combine like terms: -1x + -6x = -7x
-5 + -7x + 2x2 + -4x2 = 0

Combine like terms: 2x2 + -4x2 = -2x2
-5 + -7x + -2x2 = 0

Solving
-5 + -7x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 7x + 2x2) = 0

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

Ignore the factor -1.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-2.5, -1}

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