10x^2+19=11x^2-8x+19

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Solution for 10x^2+19=11x^2-8x+19 equation: 


Simplifying
10x2 + 19 = 11x2 + -8x + 19

Reorder the terms:
19 + 10x2 = 11x2 + -8x + 19

Reorder the terms:
19 + 10x2 = 19 + -8x + 11x2

Add '-19' to each side of the equation.
19 + -19 + 10x2 = 19 + -8x + -19 + 11x2

Combine like terms: 19 + -19 = 0
0 + 10x2 = 19 + -8x + -19 + 11x2
10x2 = 19 + -8x + -19 + 11x2

Reorder the terms:
10x2 = 19 + -19 + -8x + 11x2

Combine like terms: 19 + -19 = 0
10x2 = 0 + -8x + 11x2
10x2 = -8x + 11x2

Solving
10x2 = -8x + 11x2

Solving for variable 'x'.

Reorder the terms:
8x + 10x2 + -11x2 = -8x + 11x2 + 8x + -11x2

Combine like terms: 10x2 + -11x2 = -1x2
8x + -1x2 = -8x + 11x2 + 8x + -11x2

Reorder the terms:
8x + -1x2 = -8x + 8x + 11x2 + -11x2

Combine like terms: -8x + 8x = 0
8x + -1x2 = 0 + 11x2 + -11x2
8x + -1x2 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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