-5x^2-2x=3x-30

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Solution for -5x^2-2x=3x-30 equation: 


Simplifying
-5x2 + -2x = 3x + -30

Reorder the terms:
-2x + -5x2 = 3x + -30

Reorder the terms:
-2x + -5x2 = -30 + 3x

Solving
-2x + -5x2 = -30 + 3x

Solving for variable 'x'.

Reorder the terms:
30 + -2x + -3x + -5x2 = -30 + 3x + 30 + -3x

Combine like terms: -2x + -3x = -5x
30 + -5x + -5x2 = -30 + 3x + 30 + -3x

Reorder the terms:
30 + -5x + -5x2 = -30 + 30 + 3x + -3x

Combine like terms: -30 + 30 = 0
30 + -5x + -5x2 = 0 + 3x + -3x
30 + -5x + -5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
30 + -5x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -1x + -1x2) = 0

Factor a trinomial.
5((2 + -1x)(3 + x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {2, -3}

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