-3x(x+2)-x+1=5x-14

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Solution for -3x(x+2)-x+1=5x-14 equation: 


Simplifying
-3x(x + 2) + -1x + 1 = 5x + -14

Reorder the terms:
-3x(2 + x) + -1x + 1 = 5x + -14
(2 * -3x + x * -3x) + -1x + 1 = 5x + -14
(-6x + -3x2) + -1x + 1 = 5x + -14

Reorder the terms:
1 + -6x + -1x + -3x2 = 5x + -14

Combine like terms: -6x + -1x = -7x
1 + -7x + -3x2 = 5x + -14

Reorder the terms:
1 + -7x + -3x2 = -14 + 5x

Solving
1 + -7x + -3x2 = -14 + 5x

Solving for variable 'x'.

Reorder the terms:
1 + 14 + -7x + -5x + -3x2 = -14 + 5x + 14 + -5x

Combine like terms: 1 + 14 = 15
15 + -7x + -5x + -3x2 = -14 + 5x + 14 + -5x

Combine like terms: -7x + -5x = -12x
15 + -12x + -3x2 = -14 + 5x + 14 + -5x

Reorder the terms:
15 + -12x + -3x2 = -14 + 14 + 5x + -5x

Combine like terms: -14 + 14 = 0
15 + -12x + -3x2 = 0 + 5x + -5x
15 + -12x + -3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
15 + -12x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -4x + -1x2) = 0

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

Ignore the factor 3.

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {1, -5}

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