-x^2+4x+12=-3x+24

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Solution for -x^2+4x+12=-3x+24 equation: 


Simplifying
-1x2 + 4x + 12 = -3x + 24

Reorder the terms:
12 + 4x + -1x2 = -3x + 24

Reorder the terms:
12 + 4x + -1x2 = 24 + -3x

Solving
12 + 4x + -1x2 = 24 + -3x

Solving for variable 'x'.

Reorder the terms:
12 + -24 + 4x + 3x + -1x2 = 24 + -3x + -24 + 3x

Combine like terms: 12 + -24 = -12
-12 + 4x + 3x + -1x2 = 24 + -3x + -24 + 3x

Combine like terms: 4x + 3x = 7x
-12 + 7x + -1x2 = 24 + -3x + -24 + 3x

Reorder the terms:
-12 + 7x + -1x2 = 24 + -24 + -3x + 3x

Combine like terms: 24 + -24 = 0
-12 + 7x + -1x2 = 0 + -3x + 3x
-12 + 7x + -1x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-12 + 7x + -1x2 = 0

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


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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 = {4, 3}

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