-x(x+10)-6=-3(x-2)

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Solution for -x(x+10)-6=-3(x-2) equation: 


Simplifying
-1x(x + 10) + -6 = -3(x + -2)

Reorder the terms:
-1x(10 + x) + -6 = -3(x + -2)
(10 * -1x + x * -1x) + -6 = -3(x + -2)
(-10x + -1x2) + -6 = -3(x + -2)

Reorder the terms:
-6 + -10x + -1x2 = -3(x + -2)

Reorder the terms:
-6 + -10x + -1x2 = -3(-2 + x)
-6 + -10x + -1x2 = (-2 * -3 + x * -3)
-6 + -10x + -1x2 = (6 + -3x)

Solving
-6 + -10x + -1x2 = 6 + -3x

Solving for variable 'x'.

Reorder the terms:
-6 + -6 + -10x + 3x + -1x2 = 6 + -3x + -6 + 3x

Combine like terms: -6 + -6 = -12
-12 + -10x + 3x + -1x2 = 6 + -3x + -6 + 3x

Combine like terms: -10x + 3x = -7x
-12 + -7x + -1x2 = 6 + -3x + -6 + 3x

Reorder the terms:
-12 + -7x + -1x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
-12 + -7x + -1x2 = 0 + -3x + 3x
-12 + -7x + -1x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-12 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 7x + x2) = 0

Factor a trinomial.
-1((4 + x)(3 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

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 = {-4, -3}

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