(x+1)(x-2)(x-5)=10+3x

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Solution for (x+1)(x-2)(x-5)=10+3x equation: 


Simplifying
(x + 1)(x + -2)(x + -5) = 10 + 3x

Reorder the terms:
(1 + x)(x + -2)(x + -5) = 10 + 3x

Reorder the terms:
(1 + x)(-2 + x)(x + -5) = 10 + 3x

Reorder the terms:
(1 + x)(-2 + x)(-5 + x) = 10 + 3x

Multiply (1 + x) * (-2 + x)
(1(-2 + x) + x(-2 + x))(-5 + x) = 10 + 3x
((-2 * 1 + x * 1) + x(-2 + x))(-5 + x) = 10 + 3x
((-2 + 1x) + x(-2 + x))(-5 + x) = 10 + 3x
(-2 + 1x + (-2 * x + x * x))(-5 + x) = 10 + 3x
(-2 + 1x + (-2x + x2))(-5 + x) = 10 + 3x

Combine like terms: 1x + -2x = -1x
(-2 + -1x + x2)(-5 + x) = 10 + 3x

Multiply (-2 + -1x + x2) * (-5 + x)
(-2(-5 + x) + -1x * (-5 + x) + x2(-5 + x)) = 10 + 3x
((-5 * -2 + x * -2) + -1x * (-5 + x) + x2(-5 + x)) = 10 + 3x
((10 + -2x) + -1x * (-5 + x) + x2(-5 + x)) = 10 + 3x
(10 + -2x + (-5 * -1x + x * -1x) + x2(-5 + x)) = 10 + 3x
(10 + -2x + (5x + -1x2) + x2(-5 + x)) = 10 + 3x
(10 + -2x + 5x + -1x2 + (-5 * x2 + x * x2)) = 10 + 3x
(10 + -2x + 5x + -1x2 + (-5x2 + x3)) = 10 + 3x

Combine like terms: -2x + 5x = 3x
(10 + 3x + -1x2 + -5x2 + x3) = 10 + 3x

Combine like terms: -1x2 + -5x2 = -6x2
(10 + 3x + -6x2 + x3) = 10 + 3x

Add '-10' to each side of the equation.
10 + 3x + -6x2 + -10 + x3 = 10 + -10 + 3x

Reorder the terms:
10 + -10 + 3x + -6x2 + x3 = 10 + -10 + 3x

Combine like terms: 10 + -10 = 0
0 + 3x + -6x2 + x3 = 10 + -10 + 3x
3x + -6x2 + x3 = 10 + -10 + 3x

Combine like terms: 10 + -10 = 0
3x + -6x2 + x3 = 0 + 3x
3x + -6x2 + x3 = 3x

Add '-3x' to each side of the equation.
3x + -6x2 + -3x + x3 = 3x + -3x

Reorder the terms:
3x + -3x + -6x2 + x3 = 3x + -3x

Combine like terms: 3x + -3x = 0
0 + -6x2 + x3 = 3x + -3x
-6x2 + x3 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6x2 + x3 = 0

Solving
-6x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-6 + x) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, 6}

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