3x^2+x=(x-2)(x+5)x

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


Simplifying
3x2 + x = (x + -2)(x + 5) * x

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

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

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

Reorder the terms for easier multiplication:
x + 3x2 = x(-2 + x)(5 + x)

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

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

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

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

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

Solving
x = -10x + x3

Solving for variable 'x'.

Combine like terms: x + 10x = 11x
11x + -1x3 = -10x + x3 + 10x + -1x3

Reorder the terms:
11x + -1x3 = -10x + 10x + x3 + -1x3

Combine like terms: -10x + 10x = 0
11x + -1x3 = 0 + x3 + -1x3
11x + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
11x + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(11 + -1x2) = 0


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 '(11 + -1x2)' equal to zero and attempt to solve:

Simplifying
11 + -1x2 = 0

Solving
11 + -1x2 = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x2 = 0 + -11
-1x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-1x2 = -11

Divide each side by '-1'.
x2 = 11

Simplifying
x2 = 11

Take the square root of each side:
x = {-3.31662479, 3.31662479}
Solution
x = {0, -3.31662479, 3.31662479}

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