4x^2+6x+2=2x+5

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


Simplifying
4x2 + 6x + 2 = 2x + 5

Reorder the terms:
2 + 6x + 4x2 = 2x + 5

Reorder the terms:
2 + 6x + 4x2 = 5 + 2x

Solving
2 + 6x + 4x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
2 + -5 + 6x + -2x + 4x2 = 5 + 2x + -5 + -2x

Combine like terms: 2 + -5 = -3
-3 + 6x + -2x + 4x2 = 5 + 2x + -5 + -2x

Combine like terms: 6x + -2x = 4x
-3 + 4x + 4x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-3 + 4x + 4x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-3 + 4x + 4x2 = 0 + 2x + -2x
-3 + 4x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + 4x + 4x2 = 0

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


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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, 0.5}

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