4x^2-17x+31=3x+10

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Solution for 4x^2-17x+31=3x+10 equation: 


Simplifying
4x2 + -17x + 31 = 3x + 10

Reorder the terms:
31 + -17x + 4x2 = 3x + 10

Reorder the terms:
31 + -17x + 4x2 = 10 + 3x

Solving
31 + -17x + 4x2 = 10 + 3x

Solving for variable 'x'.

Reorder the terms:
31 + -10 + -17x + -3x + 4x2 = 10 + 3x + -10 + -3x

Combine like terms: 31 + -10 = 21
21 + -17x + -3x + 4x2 = 10 + 3x + -10 + -3x

Combine like terms: -17x + -3x = -20x
21 + -20x + 4x2 = 10 + 3x + -10 + -3x

Reorder the terms:
21 + -20x + 4x2 = 10 + -10 + 3x + -3x

Combine like terms: 10 + -10 = 0
21 + -20x + 4x2 = 0 + 3x + -3x
21 + -20x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
21 + -20x + 4x2 = 0

Factor a trinomial.
(3 + -2x)(7 + -2x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, 3.5}

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