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Simplifying (-3 + x)(-7 + x) = 0 Multiply (-3 + x) * (-7 + x) (-3(-7 + x) + x(-7 + x)) = 0 ((-7 * -3 + x * -3) + x(-7 + x)) = 0 ((21 + -3x) + x(-7 + x)) = 0 (21 + -3x + (-7 * x + x * x)) = 0 (21 + -3x + (-7x + x2)) = 0 Combine like terms: -3x + -7x = -10x (21 + -10x + x2) = 0 Solving 21 + -10x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -1x)(7 + -1x) = 0Subproblem 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 = 3Subproblem 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 = 7Solution
x = {3, 7}
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