(x-3)(x+2)=6

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Solution for (x-3)(x+2)=6 equation:


Simplifying
(x + -3)(x + 2) = 6

Reorder the terms:
(-3 + x)(x + 2) = 6

Reorder the terms:
(-3 + x)(2 + x) = 6

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

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

Solving
-6 + -1x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + -6 + -1x + x2 = 6 + -6

Combine like terms: -6 + -6 = -12
-12 + -1x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-3, 4}

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