-3x^2-5x-3=6x+7

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Solution for -3x^2-5x-3=6x+7 equation: 


Simplifying
-3x2 + -5x + -3 = 6x + 7

Reorder the terms:
-3 + -5x + -3x2 = 6x + 7

Reorder the terms:
-3 + -5x + -3x2 = 7 + 6x

Solving
-3 + -5x + -3x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
-3 + -7 + -5x + -6x + -3x2 = 7 + 6x + -7 + -6x

Combine like terms: -3 + -7 = -10
-10 + -5x + -6x + -3x2 = 7 + 6x + -7 + -6x

Combine like terms: -5x + -6x = -11x
-10 + -11x + -3x2 = 7 + 6x + -7 + -6x

Reorder the terms:
-10 + -11x + -3x2 = 7 + -7 + 6x + -6x

Combine like terms: 7 + -7 = 0
-10 + -11x + -3x2 = 0 + 6x + -6x
-10 + -11x + -3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-10 + -11x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 11x + 3x2) = 0

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

Ignore the factor -1.

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3x = 0 + -5

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

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

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {-2, -1.666666667}

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