6x+14=-2x(-3x-7)

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Solution for 6x+14=-2x(-3x-7) equation: 


Simplifying
6x + 14 = -2x(-3x + -7)

Reorder the terms:
14 + 6x = -2x(-3x + -7)

Reorder the terms:
14 + 6x = -2x(-7 + -3x)
14 + 6x = (-7 * -2x + -3x * -2x)
14 + 6x = (14x + 6x2)

Solving
14 + 6x = 14x + 6x2

Solving for variable 'x'.

Combine like terms: 6x + -14x = -8x
14 + -8x + -6x2 = 14x + 6x2 + -14x + -6x2

Reorder the terms:
14 + -8x + -6x2 = 14x + -14x + 6x2 + -6x2

Combine like terms: 14x + -14x = 0
14 + -8x + -6x2 = 0 + 6x2 + -6x2
14 + -8x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
14 + -8x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -4x + -3x2) = 0

Factor a trinomial.
2((1 + -1x)(7 + 3x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, -2.333333333}

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