5x^2-19x=-2x^2-3x-4

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Solution for 5x^2-19x=-2x^2-3x-4 equation: 


Simplifying
5x2 + -19x = -2x2 + -3x + -4

Reorder the terms:
-19x + 5x2 = -2x2 + -3x + -4

Reorder the terms:
-19x + 5x2 = -4 + -3x + -2x2

Solving
-19x + 5x2 = -4 + -3x + -2x2

Solving for variable 'x'.

Reorder the terms:
4 + -19x + 3x + 5x2 + 2x2 = -4 + -3x + -2x2 + 4 + 3x + 2x2

Combine like terms: -19x + 3x = -16x
4 + -16x + 5x2 + 2x2 = -4 + -3x + -2x2 + 4 + 3x + 2x2

Combine like terms: 5x2 + 2x2 = 7x2
4 + -16x + 7x2 = -4 + -3x + -2x2 + 4 + 3x + 2x2

Reorder the terms:
4 + -16x + 7x2 = -4 + 4 + -3x + 3x + -2x2 + 2x2

Combine like terms: -4 + 4 = 0
4 + -16x + 7x2 = 0 + -3x + 3x + -2x2 + 2x2
4 + -16x + 7x2 = -3x + 3x + -2x2 + 2x2

Combine like terms: -3x + 3x = 0
4 + -16x + 7x2 = 0 + -2x2 + 2x2
4 + -16x + 7x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
4 + -16x + 7x2 = 0

Factor a trinomial.
(2 + -7x)(2 + -1x) = 0


Subproblem 1
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857

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 = {0.2857142857, 2}

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