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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 31 + -4 = 27
27 + -21x + -3x + 4x2 = 4 + 3x + -4 + -3x

Combine like terms: -21x + -3x = -24x
27 + -24x + 4x2 = 4 + 3x + -4 + -3x

Reorder the terms:
27 + -24x + 4x2 = 4 + -4 + 3x + -3x

Combine like terms: 4 + -4 = 0
27 + -24x + 4x2 = 0 + 3x + -3x
27 + -24x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
27 + -24x + 4x2 = 0

Factor a trinomial.
(3 + -2x)(9 + -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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {1.5, 4.5}

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