4x^2-19x+55=9x+10

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Solution for 4x^2-19x+55=9x+10 equation: 


Simplifying
4x2 + -19x + 55 = 9x + 10

Reorder the terms:
55 + -19x + 4x2 = 9x + 10

Reorder the terms:
55 + -19x + 4x2 = 10 + 9x

Solving
55 + -19x + 4x2 = 10 + 9x

Solving for variable 'x'.

Reorder the terms:
55 + -10 + -19x + -9x + 4x2 = 10 + 9x + -10 + -9x

Combine like terms: 55 + -10 = 45
45 + -19x + -9x + 4x2 = 10 + 9x + -10 + -9x

Combine like terms: -19x + -9x = -28x
45 + -28x + 4x2 = 10 + 9x + -10 + -9x

Reorder the terms:
45 + -28x + 4x2 = 10 + -10 + 9x + -9x

Combine like terms: 10 + -10 = 0
45 + -28x + 4x2 = 0 + 9x + -9x
45 + -28x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
45 + -28x + 4x2 = 0

Factor a trinomial.
(5 + -2x)(9 + -2x) = 0


Subproblem 1
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

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

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {2.5, 4.5}

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