4x^2-11x+13=9x+4

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Solution for 4x^2-11x+13=9x+4 equation: 


Simplifying
4x2 + -11x + 13 = 9x + 4

Reorder the terms:
13 + -11x + 4x2 = 9x + 4

Reorder the terms:
13 + -11x + 4x2 = 4 + 9x

Solving
13 + -11x + 4x2 = 4 + 9x

Solving for variable 'x'.

Reorder the terms:
13 + -4 + -11x + -9x + 4x2 = 4 + 9x + -4 + -9x

Combine like terms: 13 + -4 = 9
9 + -11x + -9x + 4x2 = 4 + 9x + -4 + -9x

Combine like terms: -11x + -9x = -20x
9 + -20x + 4x2 = 4 + 9x + -4 + -9x

Reorder the terms:
9 + -20x + 4x2 = 4 + -4 + 9x + -9x

Combine like terms: 4 + -4 = 0
9 + -20x + 4x2 = 0 + 9x + -9x
9 + -20x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
9 + -20x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(9 + -2x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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 = {0.5, 4.5}

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