(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

Add '6' to each side of the equation.
-6 + -1x + 6 + x2 = -6 + 6

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

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

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

Solving
-1x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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 = {0, 1}

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