6x^2-4x+5=7x+1

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Solution for 6x^2-4x+5=7x+1 equation: 


Simplifying
6x2 + -4x + 5 = 7x + 1

Reorder the terms:
5 + -4x + 6x2 = 7x + 1

Reorder the terms:
5 + -4x + 6x2 = 1 + 7x

Solving
5 + -4x + 6x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
5 + -1 + -4x + -7x + 6x2 = 1 + 7x + -1 + -7x

Combine like terms: 5 + -1 = 4
4 + -4x + -7x + 6x2 = 1 + 7x + -1 + -7x

Combine like terms: -4x + -7x = -11x
4 + -11x + 6x2 = 1 + 7x + -1 + -7x

Reorder the terms:
4 + -11x + 6x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
4 + -11x + 6x2 = 0 + 7x + -7x
4 + -11x + 6x2 = 7x + -7x

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

Factor a trinomial.
(1 + -2x)(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0.5, 1.333333333}

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