4x^2+5x-24=21-6x

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Solution for 4x^2+5x-24=21-6x equation: 


Simplifying
4x2 + 5x + -24 = 21 + -6x

Reorder the terms:
-24 + 5x + 4x2 = 21 + -6x

Solving
-24 + 5x + 4x2 = 21 + -6x

Solving for variable 'x'.

Reorder the terms:
-24 + -21 + 5x + 6x + 4x2 = 21 + -6x + -21 + 6x

Combine like terms: -24 + -21 = -45
-45 + 5x + 6x + 4x2 = 21 + -6x + -21 + 6x

Combine like terms: 5x + 6x = 11x
-45 + 11x + 4x2 = 21 + -6x + -21 + 6x

Reorder the terms:
-45 + 11x + 4x2 = 21 + -21 + -6x + 6x

Combine like terms: 21 + -21 = 0
-45 + 11x + 4x2 = 0 + -6x + 6x
-45 + 11x + 4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-45 + 11x + 4x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -4x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-5, 2.25}

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