2x^2-22x=-4x^2-5x-10

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Solution for 2x^2-22x=-4x^2-5x-10 equation: 


Simplifying
2x2 + -22x = -4x2 + -5x + -10

Reorder the terms:
-22x + 2x2 = -4x2 + -5x + -10

Reorder the terms:
-22x + 2x2 = -10 + -5x + -4x2

Solving
-22x + 2x2 = -10 + -5x + -4x2

Solving for variable 'x'.

Reorder the terms:
10 + -22x + 5x + 2x2 + 4x2 = -10 + -5x + -4x2 + 10 + 5x + 4x2

Combine like terms: -22x + 5x = -17x
10 + -17x + 2x2 + 4x2 = -10 + -5x + -4x2 + 10 + 5x + 4x2

Combine like terms: 2x2 + 4x2 = 6x2
10 + -17x + 6x2 = -10 + -5x + -4x2 + 10 + 5x + 4x2

Reorder the terms:
10 + -17x + 6x2 = -10 + 10 + -5x + 5x + -4x2 + 4x2

Combine like terms: -10 + 10 = 0
10 + -17x + 6x2 = 0 + -5x + 5x + -4x2 + 4x2
10 + -17x + 6x2 = -5x + 5x + -4x2 + 4x2

Combine like terms: -5x + 5x = 0
10 + -17x + 6x2 = 0 + -4x2 + 4x2
10 + -17x + 6x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
10 + -17x + 6x2 = 0

Factor a trinomial.
(5 + -6x)(2 + -1x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.8333333333, 2}

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