4X^2-19X+43=6X+7

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Solution for 4X^2-19X+43=6X+7 equation: 


Simplifying
4X2 + -19X + 43 = 6X + 7

Reorder the terms:
43 + -19X + 4X2 = 6X + 7

Reorder the terms:
43 + -19X + 4X2 = 7 + 6X

Solving
43 + -19X + 4X2 = 7 + 6X

Solving for variable 'X'.

Reorder the terms:
43 + -7 + -19X + -6X + 4X2 = 7 + 6X + -7 + -6X

Combine like terms: 43 + -7 = 36
36 + -19X + -6X + 4X2 = 7 + 6X + -7 + -6X

Combine like terms: -19X + -6X = -25X
36 + -25X + 4X2 = 7 + 6X + -7 + -6X

Reorder the terms:
36 + -25X + 4X2 = 7 + -7 + 6X + -6X

Combine like terms: 7 + -7 = 0
36 + -25X + 4X2 = 0 + 6X + -6X
36 + -25X + 4X2 = 6X + -6X

Combine like terms: 6X + -6X = 0
36 + -25X + 4X2 = 0

Factor a trinomial.
(9 + -4X)(4 + -1X) = 0


Subproblem 1
Set the factor '(9 + -4X)' equal to zero and attempt to solve:

Simplifying
9 + -4X = 0

Solving
9 + -4X = 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 + -4X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4X = 0 + -9
-4X = 0 + -9

Combine like terms: 0 + -9 = -9
-4X = -9

Divide each side by '-4'.
X = 2.25

Simplifying
X = 2.25

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 = {2.25, 4}

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