x(-3x+5)(x-5)=7x

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Solution for x(-3x+5)(x-5)=7x equation: 


Simplifying
x(-3x + 5)(x + -5) = 7x

Reorder the terms:
x(5 + -3x)(x + -5) = 7x

Reorder the terms:
x(5 + -3x)(-5 + x) = 7x

Multiply (5 + -3x) * (-5 + x)
x(5(-5 + x) + -3x * (-5 + x)) = 7x
x((-5 * 5 + x * 5) + -3x * (-5 + x)) = 7x
x((-25 + 5x) + -3x * (-5 + x)) = 7x
x(-25 + 5x + (-5 * -3x + x * -3x)) = 7x
x(-25 + 5x + (15x + -3x2)) = 7x

Combine like terms: 5x + 15x = 20x
x(-25 + 20x + -3x2) = 7x
(-25 * x + 20x * x + -3x2 * x) = 7x
(-25x + 20x2 + -3x3) = 7x

Solving
-25x + 20x2 + -3x3 = 7x

Solving for variable 'x'.

Reorder the terms:
-25x + -7x + 20x2 + -3x3 = 7x + -7x

Combine like terms: -25x + -7x = -32x
-32x + 20x2 + -3x3 = 7x + -7x

Combine like terms: 7x + -7x = 0
-32x + 20x2 + -3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-32 + 20x + -3x2) = 0

Factor a trinomial.
x((-4 + x)(8 + -3x)) = 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 '(-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 3
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {0, 4, 2.666666667}

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