4x^2-19x+5=-2x+1

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Solution for 4x^2-19x+5=-2x+1 equation: 


Simplifying
4x2 + -19x + 5 = -2x + 1

Reorder the terms:
5 + -19x + 4x2 = -2x + 1

Reorder the terms:
5 + -19x + 4x2 = 1 + -2x

Solving
5 + -19x + 4x2 = 1 + -2x

Solving for variable 'x'.

Reorder the terms:
5 + -1 + -19x + 2x + 4x2 = 1 + -2x + -1 + 2x

Combine like terms: 5 + -1 = 4
4 + -19x + 2x + 4x2 = 1 + -2x + -1 + 2x

Combine like terms: -19x + 2x = -17x
4 + -17x + 4x2 = 1 + -2x + -1 + 2x

Reorder the terms:
4 + -17x + 4x2 = 1 + -1 + -2x + 2x

Combine like terms: 1 + -1 = 0
4 + -17x + 4x2 = 0 + -2x + 2x
4 + -17x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
4 + -17x + 4x2 = 0

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


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.25, 4}

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