2x^2+4x-6=24-3x

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Solution for 2x^2+4x-6=24-3x equation: 


Simplifying
2x2 + 4x + -6 = 24 + -3x

Reorder the terms:
-6 + 4x + 2x2 = 24 + -3x

Solving
-6 + 4x + 2x2 = 24 + -3x

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + 4x + 3x + 2x2 = 24 + -3x + -24 + 3x

Combine like terms: -6 + -24 = -30
-30 + 4x + 3x + 2x2 = 24 + -3x + -24 + 3x

Combine like terms: 4x + 3x = 7x
-30 + 7x + 2x2 = 24 + -3x + -24 + 3x

Reorder the terms:
-30 + 7x + 2x2 = 24 + -24 + -3x + 3x

Combine like terms: 24 + -24 = 0
-30 + 7x + 2x2 = 0 + -3x + 3x
-30 + 7x + 2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-30 + 7x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-6, 2.5}

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