(X-2)(X+1)-4=0

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


Simplifying
(X + -2)(X + 1) + -4 = 0

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

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

Multiply (-2 + X) * (1 + X)
(-2(1 + X) + X(1 + X)) + -4 = 0
((1 * -2 + X * -2) + X(1 + X)) + -4 = 0
((-2 + -2X) + X(1 + X)) + -4 = 0
(-2 + -2X + (1 * X + X * X)) + -4 = 0
(-2 + -2X + (1X + X2)) + -4 = 0

Combine like terms: -2X + 1X = -1X
(-2 + -1X + X2) + -4 = 0

Reorder the terms:
-2 + -4 + -1X + X2 = 0

Combine like terms: -2 + -4 = -6
-6 + -1X + X2 = 0

Solving
-6 + -1X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-2 + -1X)(3 + -1X) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -1X)' equal to zero and attempt to solve: Simplifying 3 + -1X = 0 Solving 3 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1X = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1X = 0 + -3 -1X = 0 + -3 Combine like terms: 0 + -3 = -3 -1X = -3 Divide each side by '-1'. X = 3 Simplifying X = 3

Solution

X = {-2, 3}

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