X(X-4)-21=0

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Solution for X(X-4)-21=0 equation:


Simplifying
X(X + -4) + -21 = 0

Reorder the terms:
X(-4 + X) + -21 = 0
(-4 * X + X * X) + -21 = 0
(-4X + X2) + -21 = 0

Reorder the terms:
-21 + -4X + X2 = 0

Solving
-21 + -4X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-3 + -1X)(7 + -1X) = 0

Subproblem 1

Set the factor '(-3 + -1X)' equal to zero and attempt to solve: Simplifying -3 + -1X = 0 Solving -3 + -1X = 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 + -1X = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1X = 0 + 3 -1X = 0 + 3 Combine like terms: 0 + 3 = 3 -1X = 3 Divide each side by '-1'. X = -3 Simplifying X = -3

Subproblem 2

Set the factor '(7 + -1X)' equal to zero and attempt to solve: Simplifying 7 + -1X = 0 Solving 7 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1X = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1X = 0 + -7 -1X = 0 + -7 Combine like terms: 0 + -7 = -7 -1X = -7 Divide each side by '-1'. X = 7 Simplifying X = 7

Solution

X = {-3, 7}

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