3x^2+4x=5x+14

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Solution for 3x^2+4x=5x+14 equation: 


Simplifying
3x2 + 4x = 5x + 14

Reorder the terms:
4x + 3x2 = 5x + 14

Reorder the terms:
4x + 3x2 = 14 + 5x

Solving
4x + 3x2 = 14 + 5x

Solving for variable 'x'.

Reorder the terms:
-14 + 4x + -5x + 3x2 = 14 + 5x + -14 + -5x

Combine like terms: 4x + -5x = -1x
-14 + -1x + 3x2 = 14 + 5x + -14 + -5x

Reorder the terms:
-14 + -1x + 3x2 = 14 + -14 + 5x + -5x

Combine like terms: 14 + -14 = 0
-14 + -1x + 3x2 = 0 + 5x + -5x
-14 + -1x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-14 + -1x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(7 + -3x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-2, 2.333333333}

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