(x-3)(x+4)=-6

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Solution for (x-3)(x+4)=-6 equation: 


Simplifying
(x + -3)(x + 4) = -6

Reorder the terms:
(-3 + x)(x + 4) = -6

Reorder the terms:
(-3 + x)(4 + x) = -6

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = -6
((4 * -3 + x * -3) + x(4 + x)) = -6
((-12 + -3x) + x(4 + x)) = -6
(-12 + -3x + (4 * x + x * x)) = -6
(-12 + -3x + (4x + x2)) = -6

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = -6

Solving
-12 + 1x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-12 + 6 + 1x + x2 = -6 + 6

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

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

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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