6x^2+3x=-7x-4

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Solution for 6x^2+3x=-7x-4 equation: 


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 3x + 7x = 10x
4 + 10x + 6x2 = -4 + -7x + 4 + 7x

Reorder the terms:
4 + 10x + 6x2 = -4 + 4 + -7x + 7x

Combine like terms: -4 + 4 = 0
4 + 10x + 6x2 = 0 + -7x + 7x
4 + 10x + 6x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
4 + 10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 5x + 3x2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-1, -0.6666666667}

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