4x^2-13x+19=4x+1

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Solution for 4x^2-13x+19=4x+1 equation: 


Simplifying
4x2 + -13x + 19 = 4x + 1

Reorder the terms:
19 + -13x + 4x2 = 4x + 1

Reorder the terms:
19 + -13x + 4x2 = 1 + 4x

Solving
19 + -13x + 4x2 = 1 + 4x

Solving for variable 'x'.

Reorder the terms:
19 + -1 + -13x + -4x + 4x2 = 1 + 4x + -1 + -4x

Combine like terms: 19 + -1 = 18
18 + -13x + -4x + 4x2 = 1 + 4x + -1 + -4x

Combine like terms: -13x + -4x = -17x
18 + -17x + 4x2 = 1 + 4x + -1 + -4x

Reorder the terms:
18 + -17x + 4x2 = 1 + -1 + 4x + -4x

Combine like terms: 1 + -1 = 0
18 + -17x + 4x2 = 0 + 4x + -4x
18 + -17x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 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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