4x^2-5x+14=6x+7

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Solution for 4x^2-5x+14=6x+7 equation: 


Simplifying
4x2 + -5x + 14 = 6x + 7

Reorder the terms:
14 + -5x + 4x2 = 6x + 7

Reorder the terms:
14 + -5x + 4x2 = 7 + 6x

Solving
14 + -5x + 4x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
14 + -7 + -5x + -6x + 4x2 = 7 + 6x + -7 + -6x

Combine like terms: 14 + -7 = 7
7 + -5x + -6x + 4x2 = 7 + 6x + -7 + -6x

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

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

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

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

Factor a trinomial.
(1 + -1x)(7 + -4x) = 0


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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {1, 1.75}

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