4x^2-21x+24=2x+9

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Solution for 4x^2-21x+24=2x+9 equation: 


Simplifying
4x2 + -21x + 24 = 2x + 9

Reorder the terms:
24 + -21x + 4x2 = 2x + 9

Reorder the terms:
24 + -21x + 4x2 = 9 + 2x

Solving
24 + -21x + 4x2 = 9 + 2x

Solving for variable 'x'.

Reorder the terms:
24 + -9 + -21x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: 24 + -9 = 15
15 + -21x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: -21x + -2x = -23x
15 + -23x + 4x2 = 9 + 2x + -9 + -2x

Reorder the terms:
15 + -23x + 4x2 = 9 + -9 + 2x + -2x

Combine like terms: 9 + -9 = 0
15 + -23x + 4x2 = 0 + 2x + -2x
15 + -23x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
15 + -23x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(5 + -1x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

Subproblem 2
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
Solution
x = {0.75, 5}

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