4x^2-13x+22=4x+7

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Solution for 4x^2-13x+22=4x+7 equation: 


Simplifying
4x2 + -13x + 22 = 4x + 7

Reorder the terms:
22 + -13x + 4x2 = 4x + 7

Reorder the terms:
22 + -13x + 4x2 = 7 + 4x

Solving
22 + -13x + 4x2 = 7 + 4x

Solving for variable 'x'.

Reorder the terms:
22 + -7 + -13x + -4x + 4x2 = 7 + 4x + -7 + -4x

Combine like terms: 22 + -7 = 15
15 + -13x + -4x + 4x2 = 7 + 4x + -7 + -4x

Combine like terms: -13x + -4x = -17x
15 + -17x + 4x2 = 7 + 4x + -7 + -4x

Reorder the terms:
15 + -17x + 4x2 = 7 + -7 + 4x + -4x

Combine like terms: 7 + -7 = 0
15 + -17x + 4x2 = 0 + 4x + -4x
15 + -17x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
15 + -17x + 4x2 = 0

Factor a trinomial.
(5 + -4x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.25, 3}

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