4x^2-5x+13=6x+7

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Solution for 4x^2-5x+13=6x+7 equation: 


Simplifying
4x2 + -5x + 13 = 6x + 7

Reorder the terms:
13 + -5x + 4x2 = 6x + 7

Reorder the terms:
13 + -5x + 4x2 = 7 + 6x

Solving
13 + -5x + 4x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
13 + -7 + -5x + -6x + 4x2 = 7 + 6x + -7 + -6x

Combine like terms: 13 + -7 = 6
6 + -5x + -6x + 4x2 = 7 + 6x + -7 + -6x

Combine like terms: -5x + -6x = -11x
6 + -11x + 4x2 = 7 + 6x + -7 + -6x

Reorder the terms:
6 + -11x + 4x2 = 7 + -7 + 6x + -6x

Combine like terms: 7 + -7 = 0
6 + -11x + 4x2 = 0 + 6x + -6x
6 + -11x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
6 + -11x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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 = {0.75, 2}

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