105x^2+388x=-343-4x

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Solution for 105x^2+388x=-343-4x equation: 


Simplifying
105x2 + 388x = -343 + -4x

Reorder the terms:
388x + 105x2 = -343 + -4x

Solving
388x + 105x2 = -343 + -4x

Solving for variable 'x'.

Reorder the terms:
343 + 388x + 4x + 105x2 = -343 + -4x + 343 + 4x

Combine like terms: 388x + 4x = 392x
343 + 392x + 105x2 = -343 + -4x + 343 + 4x

Reorder the terms:
343 + 392x + 105x2 = -343 + 343 + -4x + 4x

Combine like terms: -343 + 343 = 0
343 + 392x + 105x2 = 0 + -4x + 4x
343 + 392x + 105x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
343 + 392x + 105x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(49 + 56x + 15x2) = 0

Factor a trinomial.
7((7 + 3x)(7 + 5x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4
Solution
x = {-2.333333333, -1.4}

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