-27+62x=-3-2x-24x^2

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Solution for -27+62x=-3-2x-24x^2 equation: 


Simplifying
-27 + 62x = -3 + -2x + -24x2

Solving
-27 + 62x = -3 + -2x + -24x2

Solving for variable 'x'.

Reorder the terms:
-27 + 3 + 62x + 2x + 24x2 = -3 + -2x + -24x2 + 3 + 2x + 24x2

Combine like terms: -27 + 3 = -24
-24 + 62x + 2x + 24x2 = -3 + -2x + -24x2 + 3 + 2x + 24x2

Combine like terms: 62x + 2x = 64x
-24 + 64x + 24x2 = -3 + -2x + -24x2 + 3 + 2x + 24x2

Reorder the terms:
-24 + 64x + 24x2 = -3 + 3 + -2x + 2x + -24x2 + 24x2

Combine like terms: -3 + 3 = 0
-24 + 64x + 24x2 = 0 + -2x + 2x + -24x2 + 24x2
-24 + 64x + 24x2 = -2x + 2x + -24x2 + 24x2

Combine like terms: -2x + 2x = 0
-24 + 64x + 24x2 = 0 + -24x2 + 24x2
-24 + 64x + 24x2 = -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
-24 + 64x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + 8x + 3x2) = 0

Factor a trinomial.
8((-3 + -1x)(1 + -3x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-3, 0.3333333333}

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