-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 = 4
4 + -5x + -6x + -3x2 = -7 + 6x + 7 + -6x

Combine like terms: -5x + -6x = -11x
4 + -11x + -3x2 = -7 + 6x + 7 + -6x

Reorder the terms:
4 + -11x + -3x2 = -7 + 7 + 6x + -6x

Combine like terms: -7 + 7 = 0
4 + -11x + -3x2 = 0 + 6x + -6x
4 + -11x + -3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
4 + -11x + -3x2 = 0

Factor a trinomial.
(1 + -3x)(4 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0.3333333333, -4}

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