(x-5)(5x+1)=-5

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Solution for (x-5)(5x+1)=-5 equation:


Simplifying
(x + -5)(5x + 1) = -5

Reorder the terms:
(-5 + x)(5x + 1) = -5

Reorder the terms:
(-5 + x)(1 + 5x) = -5

Multiply (-5 + x) * (1 + 5x)
(-5(1 + 5x) + x(1 + 5x)) = -5
((1 * -5 + 5x * -5) + x(1 + 5x)) = -5
((-5 + -25x) + x(1 + 5x)) = -5
(-5 + -25x + (1 * x + 5x * x)) = -5
(-5 + -25x + (1x + 5x2)) = -5

Combine like terms: -25x + 1x = -24x
(-5 + -24x + 5x2) = -5

Add '5' to each side of the equation.
-5 + -24x + 5 + 5x2 = -5 + 5

Reorder the terms:
-5 + 5 + -24x + 5x2 = -5 + 5

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

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

Solving
-24x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + 5x) = 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 '(-24 + 5x)' equal to zero and attempt to solve: Simplifying -24 + 5x = 0 Solving -24 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + 5x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 5x = 0 + 24 5x = 0 + 24 Combine like terms: 0 + 24 = 24 5x = 24 Divide each side by '5'. x = 4.8 Simplifying x = 4.8

Solution

x = {0, 4.8}

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