4x^2-5x-5=2x^2+4x

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


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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(-1 + -2x)(5 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.5, 5}

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