4x^2-21x+31=2x+3

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Solution for 4x^2-21x+31=2x+3 equation: 


Simplifying
4x2 + -21x + 31 = 2x + 3

Reorder the terms:
31 + -21x + 4x2 = 2x + 3

Reorder the terms:
31 + -21x + 4x2 = 3 + 2x

Solving
31 + -21x + 4x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
31 + -3 + -21x + -2x + 4x2 = 3 + 2x + -3 + -2x

Combine like terms: 31 + -3 = 28
28 + -21x + -2x + 4x2 = 3 + 2x + -3 + -2x

Combine like terms: -21x + -2x = -23x
28 + -23x + 4x2 = 3 + 2x + -3 + -2x

Reorder the terms:
28 + -23x + 4x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
28 + -23x + 4x2 = 0 + 2x + -2x
28 + -23x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
28 + -23x + 4x2 = 0

Factor a trinomial.
(7 + -4x)(4 + -1x) = 0


Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75

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 = {1.75, 4}

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