0=x^2-5x^2+4x

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Solution for 0=x^2-5x^2+4x equation:


Simplifying
0 = x2 + -5x2 + 4x

Reorder the terms:
0 = 4x + x2 + -5x2

Combine like terms: x2 + -5x2 = -4x2
0 = 4x + -4x2

Solving
0 = 4x + -4x2

Solving for variable 'x'.
Remove the zero:
-4x + 4x2 = 4x + -4x2 + -4x + 4x2

Reorder the terms:
-4x + 4x2 = 4x + -4x + -4x2 + 4x2

Combine like terms: 4x + -4x = 0
-4x + 4x2 = 0 + -4x2 + 4x2
-4x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-1 + x) = 0

Ignore the factor 4.

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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1

Solution

x = {0, 1}

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