x^2+7x=24-3x

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Solution for x^2+7x=24-3x equation: 


Simplifying
x2 + 7x = 24 + -3x

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

Solving
7x + x2 = 24 + -3x

Solving for variable 'x'.

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

Combine like terms: 7x + 3x = 10x
-24 + 10x + x2 = 24 + -3x + -24 + 3x

Reorder the terms:
-24 + 10x + x2 = 24 + -24 + -3x + 3x

Combine like terms: 24 + -24 = 0
-24 + 10x + x2 = 0 + -3x + 3x
-24 + 10x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-24 + 10x + x2 = 0

Factor a trinomial.
(-12 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

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

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

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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 = {-12, 2}

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