4x^2-19x+41=5x+6

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Solution for 4x^2-19x+41=5x+6 equation: 


Simplifying
4x2 + -19x + 41 = 5x + 6

Reorder the terms:
41 + -19x + 4x2 = 5x + 6

Reorder the terms:
41 + -19x + 4x2 = 6 + 5x

Solving
41 + -19x + 4x2 = 6 + 5x

Solving for variable 'x'.

Reorder the terms:
41 + -6 + -19x + -5x + 4x2 = 6 + 5x + -6 + -5x

Combine like terms: 41 + -6 = 35
35 + -19x + -5x + 4x2 = 6 + 5x + -6 + -5x

Combine like terms: -19x + -5x = -24x
35 + -24x + 4x2 = 6 + 5x + -6 + -5x

Reorder the terms:
35 + -24x + 4x2 = 6 + -6 + 5x + -5x

Combine like terms: 6 + -6 = 0
35 + -24x + 4x2 = 0 + 5x + -5x
35 + -24x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
35 + -24x + 4x2 = 0

Factor a trinomial.
(5 + -2x)(7 + -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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {2.5, 3.5}

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