2x^2+4x+5=3x+8

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Solution for 2x^2+4x+5=3x+8 equation: 


Simplifying
2x2 + 4x + 5 = 3x + 8

Reorder the terms:
5 + 4x + 2x2 = 3x + 8

Reorder the terms:
5 + 4x + 2x2 = 8 + 3x

Solving
5 + 4x + 2x2 = 8 + 3x

Solving for variable 'x'.

Reorder the terms:
5 + -8 + 4x + -3x + 2x2 = 8 + 3x + -8 + -3x

Combine like terms: 5 + -8 = -3
-3 + 4x + -3x + 2x2 = 8 + 3x + -8 + -3x

Combine like terms: 4x + -3x = 1x
-3 + 1x + 2x2 = 8 + 3x + -8 + -3x

Reorder the terms:
-3 + 1x + 2x2 = 8 + -8 + 3x + -3x

Combine like terms: 8 + -8 = 0
-3 + 1x + 2x2 = 0 + 3x + -3x
-3 + 1x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-3 + 1x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(1 + -1x) = 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 + -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
Solution
x = {-1.5, 1}

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