4x*x-20x=-5x*x-6x-5

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Solution for 4x*x-20x=-5x*x-6x-5 equation: 


Simplifying
4x * x + -20x = -5x * x + -6x + -5

Multiply x * x
4x2 + -20x = -5x * x + -6x + -5

Reorder the terms:
-20x + 4x2 = -5x * x + -6x + -5

Multiply x * x
-20x + 4x2 = -5x2 + -6x + -5

Reorder the terms:
-20x + 4x2 = -5 + -6x + -5x2

Solving
-20x + 4x2 = -5 + -6x + -5x2

Solving for variable 'x'.

Reorder the terms:
5 + -20x + 6x + 4x2 + 5x2 = -5 + -6x + -5x2 + 5 + 6x + 5x2

Combine like terms: -20x + 6x = -14x
5 + -14x + 4x2 + 5x2 = -5 + -6x + -5x2 + 5 + 6x + 5x2

Combine like terms: 4x2 + 5x2 = 9x2
5 + -14x + 9x2 = -5 + -6x + -5x2 + 5 + 6x + 5x2

Reorder the terms:
5 + -14x + 9x2 = -5 + 5 + -6x + 6x + -5x2 + 5x2

Combine like terms: -5 + 5 = 0
5 + -14x + 9x2 = 0 + -6x + 6x + -5x2 + 5x2
5 + -14x + 9x2 = -6x + 6x + -5x2 + 5x2

Combine like terms: -6x + 6x = 0
5 + -14x + 9x2 = 0 + -5x2 + 5x2
5 + -14x + 9x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
5 + -14x + 9x2 = 0

Factor a trinomial.
(5 + -9x)(1 + -1x) = 0


Subproblem 1
Set the factor '(5 + -9x)' equal to zero and attempt to solve:

Simplifying
5 + -9x = 0

Solving
5 + -9x = 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 + -9x = 0 + -5

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

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

Divide each side by '-9'.
x = 0.5555555556

Simplifying
x = 0.5555555556

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 = {0.5555555556, 1}

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