4x^2-31x+51=-3x+6

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Solution for 4x^2-31x+51=-3x+6 equation: 


Simplifying
4x2 + -31x + 51 = -3x + 6

Reorder the terms:
51 + -31x + 4x2 = -3x + 6

Reorder the terms:
51 + -31x + 4x2 = 6 + -3x

Solving
51 + -31x + 4x2 = 6 + -3x

Solving for variable 'x'.

Reorder the terms:
51 + -6 + -31x + 3x + 4x2 = 6 + -3x + -6 + 3x

Combine like terms: 51 + -6 = 45
45 + -31x + 3x + 4x2 = 6 + -3x + -6 + 3x

Combine like terms: -31x + 3x = -28x
45 + -28x + 4x2 = 6 + -3x + -6 + 3x

Reorder the terms:
45 + -28x + 4x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
45 + -28x + 4x2 = 0 + -3x + 3x
45 + -28x + 4x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
45 + -28x + 4x2 = 0

Factor a trinomial.
(5 + -2x)(9 + -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 '(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 = {2.5, 4.5}

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