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

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


Simplifying
(x + -2)(x + 3) + (2x + 1)(x + -2) = x2 + -4

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

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

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) + (2x + 1)(x + -2) = x2 + -4
((3 * -2 + x * -2) + x(3 + x)) + (2x + 1)(x + -2) = x2 + -4
((-6 + -2x) + x(3 + x)) + (2x + 1)(x + -2) = x2 + -4
(-6 + -2x + (3 * x + x * x)) + (2x + 1)(x + -2) = x2 + -4
(-6 + -2x + (3x + x2)) + (2x + 1)(x + -2) = x2 + -4

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

Reorder the terms:
-6 + 1x + x2 + (1 + 2x)(x + -2) = x2 + -4

Reorder the terms:
-6 + 1x + x2 + (1 + 2x)(-2 + x) = x2 + -4

Multiply (1 + 2x) * (-2 + x)
-6 + 1x + x2 + (1(-2 + x) + 2x * (-2 + x)) = x2 + -4
-6 + 1x + x2 + ((-2 * 1 + x * 1) + 2x * (-2 + x)) = x2 + -4
-6 + 1x + x2 + ((-2 + 1x) + 2x * (-2 + x)) = x2 + -4
-6 + 1x + x2 + (-2 + 1x + (-2 * 2x + x * 2x)) = x2 + -4
-6 + 1x + x2 + (-2 + 1x + (-4x + 2x2)) = x2 + -4

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

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

Combine like terms: -6 + -2 = -8
-8 + 1x + -3x + x2 + 2x2 = x2 + -4

Combine like terms: 1x + -3x = -2x
-8 + -2x + x2 + 2x2 = x2 + -4

Combine like terms: x2 + 2x2 = 3x2
-8 + -2x + 3x2 = x2 + -4

Reorder the terms:
-8 + -2x + 3x2 = -4 + x2

Solving
-8 + -2x + 3x2 = -4 + x2

Solving for variable 'x'.

Reorder the terms:
-8 + 4 + -2x + 3x2 + -1x2 = -4 + x2 + 4 + -1x2

Combine like terms: -8 + 4 = -4
-4 + -2x + 3x2 + -1x2 = -4 + x2 + 4 + -1x2

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

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

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

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

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

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