4x^2-13x+13=3x+6

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Solution for 4x^2-13x+13=3x+6 equation: 


Simplifying
4x2 + -13x + 13 = 3x + 6

Reorder the terms:
13 + -13x + 4x2 = 3x + 6

Reorder the terms:
13 + -13x + 4x2 = 6 + 3x

Solving
13 + -13x + 4x2 = 6 + 3x

Solving for variable 'x'.

Reorder the terms:
13 + -6 + -13x + -3x + 4x2 = 6 + 3x + -6 + -3x

Combine like terms: 13 + -6 = 7
7 + -13x + -3x + 4x2 = 6 + 3x + -6 + -3x

Combine like terms: -13x + -3x = -16x
7 + -16x + 4x2 = 6 + 3x + -6 + -3x

Reorder the terms:
7 + -16x + 4x2 = 6 + -6 + 3x + -3x

Combine like terms: 6 + -6 = 0
7 + -16x + 4x2 = 0 + 3x + -3x
7 + -16x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
7 + -16x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(7 + -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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0.5, 3.5}

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