4x(x+6)-x^2=5x^2

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Solution for 4x(x+6)-x^2=5x^2 equation:


Simplifying
4x(x + 6) + -1x2 = 5x2

Reorder the terms:
4x(6 + x) + -1x2 = 5x2
(6 * 4x + x * 4x) + -1x2 = 5x2
(24x + 4x2) + -1x2 = 5x2

Combine like terms: 4x2 + -1x2 = 3x2
24x + 3x2 = 5x2

Solving
24x + 3x2 = 5x2

Solving for variable 'x'.

Combine like terms: 3x2 + -5x2 = -2x2
24x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(12 + -1x) = 0

Ignore the factor 2.

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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12

Solution

x = {0, 12}

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