5x(3x-1)-4(x^2+4x)=x

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Solution for 5x(3x-1)-4(x^2+4x)=x equation:


Simplifying
5x(3x + -1) + -4(x2 + 4x) = x

Reorder the terms:
5x(-1 + 3x) + -4(x2 + 4x) = x
(-1 * 5x + 3x * 5x) + -4(x2 + 4x) = x
(-5x + 15x2) + -4(x2 + 4x) = x

Reorder the terms:
-5x + 15x2 + -4(4x + x2) = x
-5x + 15x2 + (4x * -4 + x2 * -4) = x
-5x + 15x2 + (-16x + -4x2) = x

Reorder the terms:
-5x + -16x + 15x2 + -4x2 = x

Combine like terms: -5x + -16x = -21x
-21x + 15x2 + -4x2 = x

Combine like terms: 15x2 + -4x2 = 11x2
-21x + 11x2 = x

Solving
-21x + 11x2 = x

Solving for variable 'x'.

Reorder the terms:
-21x + -1x + 11x2 = x + -1x

Combine like terms: -21x + -1x = -22x
-22x + 11x2 = x + -1x

Combine like terms: x + -1x = 0
-22x + 11x2 = 0

Factor out the Greatest Common Factor (GCF), '11x'.
11x(-2 + x) = 0

Ignore the factor 11.

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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Solution

x = {0, 2}

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