2x^2(x-5)-3x(5-x)=0

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Solution for 2x^2(x-5)-3x(5-x)=0 equation:


Simplifying
2x2(x + -5) + -3x(5 + -1x) = 0

Reorder the terms:
2x2(-5 + x) + -3x(5 + -1x) = 0
(-5 * 2x2 + x * 2x2) + -3x(5 + -1x) = 0
(-10x2 + 2x3) + -3x(5 + -1x) = 0
-10x2 + 2x3 + (5 * -3x + -1x * -3x) = 0
-10x2 + 2x3 + (-15x + 3x2) = 0

Reorder the terms:
-15x + -10x2 + 3x2 + 2x3 = 0

Combine like terms: -10x2 + 3x2 = -7x2
-15x + -7x2 + 2x3 = 0

Solving
-15x + -7x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + -7x + 2x2) = 0

Factor a trinomial.
x((-3 + -2x)(5 + -1x)) = 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 '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, -1.5, 5}

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