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

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


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

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

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

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

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