4x^2-11x+9=6x+5

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Solution for 4x^2-11x+9=6x+5 equation: 


Simplifying
4x2 + -11x + 9 = 6x + 5

Reorder the terms:
9 + -11x + 4x2 = 6x + 5

Reorder the terms:
9 + -11x + 4x2 = 5 + 6x

Solving
9 + -11x + 4x2 = 5 + 6x

Solving for variable 'x'.

Reorder the terms:
9 + -5 + -11x + -6x + 4x2 = 5 + 6x + -5 + -6x

Combine like terms: 9 + -5 = 4
4 + -11x + -6x + 4x2 = 5 + 6x + -5 + -6x

Combine like terms: -11x + -6x = -17x
4 + -17x + 4x2 = 5 + 6x + -5 + -6x

Reorder the terms:
4 + -17x + 4x2 = 5 + -5 + 6x + -6x

Combine like terms: 5 + -5 = 0
4 + -17x + 4x2 = 0 + 6x + -6x
4 + -17x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
4 + -17x + 4x2 = 0

Factor a trinomial.
(1 + -4x)(4 + -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 '(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 = {0.25, 4}

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