3x(x-2)-(x+1)(x-13)=13

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Solution for 3x(x-2)-(x+1)(x-13)=13 equation: 


Simplifying
3x(x + -2) + -1(x + 1)(x + -13) = 13

Reorder the terms:
3x(-2 + x) + -1(x + 1)(x + -13) = 13
(-2 * 3x + x * 3x) + -1(x + 1)(x + -13) = 13
(-6x + 3x2) + -1(x + 1)(x + -13) = 13

Reorder the terms:
-6x + 3x2 + -1(1 + x)(x + -13) = 13

Reorder the terms:
-6x + 3x2 + -1(1 + x)(-13 + x) = 13

Multiply (1 + x) * (-13 + x)
-6x + 3x2 + -1(1(-13 + x) + x(-13 + x)) = 13
-6x + 3x2 + -1((-13 * 1 + x * 1) + x(-13 + x)) = 13
-6x + 3x2 + -1((-13 + 1x) + x(-13 + x)) = 13
-6x + 3x2 + -1(-13 + 1x + (-13 * x + x * x)) = 13
-6x + 3x2 + -1(-13 + 1x + (-13x + x2)) = 13

Combine like terms: 1x + -13x = -12x
-6x + 3x2 + -1(-13 + -12x + x2) = 13
-6x + 3x2 + (-13 * -1 + -12x * -1 + x2 * -1) = 13
-6x + 3x2 + (13 + 12x + -1x2) = 13

Reorder the terms:
13 + -6x + 12x + 3x2 + -1x2 = 13

Combine like terms: -6x + 12x = 6x
13 + 6x + 3x2 + -1x2 = 13

Combine like terms: 3x2 + -1x2 = 2x2
13 + 6x + 2x2 = 13

Add '-13' to each side of the equation.
13 + 6x + -13 + 2x2 = 13 + -13

Reorder the terms:
13 + -13 + 6x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
0 + 6x + 2x2 = 13 + -13
6x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
6x + 2x2 = 0

Solving
6x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {0, -3}

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