4x^2-3x+11=6x+9

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Solution for 4x^2-3x+11=6x+9 equation: 


Simplifying
4x2 + -3x + 11 = 6x + 9

Reorder the terms:
11 + -3x + 4x2 = 6x + 9

Reorder the terms:
11 + -3x + 4x2 = 9 + 6x

Solving
11 + -3x + 4x2 = 9 + 6x

Solving for variable 'x'.

Reorder the terms:
11 + -9 + -3x + -6x + 4x2 = 9 + 6x + -9 + -6x

Combine like terms: 11 + -9 = 2
2 + -3x + -6x + 4x2 = 9 + 6x + -9 + -6x

Combine like terms: -3x + -6x = -9x
2 + -9x + 4x2 = 9 + 6x + -9 + -6x

Reorder the terms:
2 + -9x + 4x2 = 9 + -9 + 6x + -6x

Combine like terms: 9 + -9 = 0
2 + -9x + 4x2 = 0 + 6x + -6x
2 + -9x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
2 + -9x + 4x2 = 0

Factor a trinomial.
(1 + -4x)(2 + -1x) = 0


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
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
Solution
x = {0.25, 2}

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