4x^2-9x+24=8x+6

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Solution for 4x^2-9x+24=8x+6 equation: 


Simplifying
4x2 + -9x + 24 = 8x + 6

Reorder the terms:
24 + -9x + 4x2 = 8x + 6

Reorder the terms:
24 + -9x + 4x2 = 6 + 8x

Solving
24 + -9x + 4x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
24 + -6 + -9x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: 24 + -6 = 18
18 + -9x + -8x + 4x2 = 6 + 8x + -6 + -8x

Combine like terms: -9x + -8x = -17x
18 + -17x + 4x2 = 6 + 8x + -6 + -8x

Reorder the terms:
18 + -17x + 4x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
18 + -17x + 4x2 = 0 + 8x + -8x
18 + -17x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
18 + -17x + 4x2 = 0

Factor a trinomial.
(2 + -1x)(9 + -4x) = 0


Subproblem 1
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

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 = {2, 2.25}

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