4x^2-7x+14=2x+9

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Solution for 4x^2-7x+14=2x+9 equation: 


Simplifying
4x2 + -7x + 14 = 2x + 9

Reorder the terms:
14 + -7x + 4x2 = 2x + 9

Reorder the terms:
14 + -7x + 4x2 = 9 + 2x

Solving
14 + -7x + 4x2 = 9 + 2x

Solving for variable 'x'.

Reorder the terms:
14 + -9 + -7x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: 14 + -9 = 5
5 + -7x + -2x + 4x2 = 9 + 2x + -9 + -2x

Combine like terms: -7x + -2x = -9x
5 + -9x + 4x2 = 9 + 2x + -9 + -2x

Reorder the terms:
5 + -9x + 4x2 = 9 + -9 + 2x + -2x

Combine like terms: 9 + -9 = 0
5 + -9x + 4x2 = 0 + 2x + -2x
5 + -9x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
5 + -9x + 4x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {1, 1.25}

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