4X^2-19X+29=5X+2

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Solution for 4X^2-19X+29=5X+2 equation: 


Simplifying
4X2 + -19X + 29 = 5X + 2

Reorder the terms:
29 + -19X + 4X2 = 5X + 2

Reorder the terms:
29 + -19X + 4X2 = 2 + 5X

Solving
29 + -19X + 4X2 = 2 + 5X

Solving for variable 'X'.

Reorder the terms:
29 + -2 + -19X + -5X + 4X2 = 2 + 5X + -2 + -5X

Combine like terms: 29 + -2 = 27
27 + -19X + -5X + 4X2 = 2 + 5X + -2 + -5X

Combine like terms: -19X + -5X = -24X
27 + -24X + 4X2 = 2 + 5X + -2 + -5X

Reorder the terms:
27 + -24X + 4X2 = 2 + -2 + 5X + -5X

Combine like terms: 2 + -2 = 0
27 + -24X + 4X2 = 0 + 5X + -5X
27 + -24X + 4X2 = 5X + -5X

Combine like terms: 5X + -5X = 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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