1(x-2)(x+3)=0

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Solution for 1(x-2)(x+3)=0 equation:


Simplifying
1(x + -2)(x + 3) = 0

Reorder the terms:
1(-2 + x)(x + 3) = 0

Reorder the terms:
1(-2 + x)(3 + x) = 0

Multiply (-2 + x) * (3 + x)
1(-2(3 + x) + x(3 + x)) = 0
1((3 * -2 + x * -2) + x(3 + x)) = 0
1((-6 + -2x) + x(3 + x)) = 0
1(-6 + -2x + (3 * x + x * x)) = 0
1(-6 + -2x + (3x + x2)) = 0

Combine like terms: -2x + 3x = 1x
1(-6 + 1x + x2) = 0
(-6 * 1 + 1x * 1 + x2 * 1) = 0
(-6 + 1x + 1x2) = 0

Solving
-6 + 1x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(2 + -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 '(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 = {-3, 2}

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