2x^2-19x=-3x^2-5x-9

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Solution for 2x^2-19x=-3x^2-5x-9 equation: 


Simplifying
2x2 + -19x = -3x2 + -5x + -9

Reorder the terms:
-19x + 2x2 = -3x2 + -5x + -9

Reorder the terms:
-19x + 2x2 = -9 + -5x + -3x2

Solving
-19x + 2x2 = -9 + -5x + -3x2

Solving for variable 'x'.

Reorder the terms:
9 + -19x + 5x + 2x2 + 3x2 = -9 + -5x + -3x2 + 9 + 5x + 3x2

Combine like terms: -19x + 5x = -14x
9 + -14x + 2x2 + 3x2 = -9 + -5x + -3x2 + 9 + 5x + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
9 + -14x + 5x2 = -9 + -5x + -3x2 + 9 + 5x + 3x2

Reorder the terms:
9 + -14x + 5x2 = -9 + 9 + -5x + 5x + -3x2 + 3x2

Combine like terms: -9 + 9 = 0
9 + -14x + 5x2 = 0 + -5x + 5x + -3x2 + 3x2
9 + -14x + 5x2 = -5x + 5x + -3x2 + 3x2

Combine like terms: -5x + 5x = 0
9 + -14x + 5x2 = 0 + -3x2 + 3x2
9 + -14x + 5x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
9 + -14x + 5x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5x = 0 + -9

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

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

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {1, 1.8}

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