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

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


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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: -9x + -4x = -13x
10 + -13x + 4x2 = 9 + 4x + -9 + -4x

Reorder the terms:
10 + -13x + 4x2 = 9 + -9 + 4x + -4x

Combine like terms: 9 + -9 = 0
10 + -13x + 4x2 = 0 + 4x + -4x
10 + -13x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
10 + -13x + 4x2 = 0

Factor a trinomial.
(5 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

Subproblem 2
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
Solution
x = {1.25, 2}

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