7(x-3)(2-x)=0

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Solution for 7(x-3)(2-x)=0 equation:


Simplifying
7(x + -3)(2 + -1x) = 0

Reorder the terms:
7(-3 + x)(2 + -1x) = 0

Multiply (-3 + x) * (2 + -1x)
7(-3(2 + -1x) + x(2 + -1x)) = 0
7((2 * -3 + -1x * -3) + x(2 + -1x)) = 0
7((-6 + 3x) + x(2 + -1x)) = 0
7(-6 + 3x + (2 * x + -1x * x)) = 0
7(-6 + 3x + (2x + -1x2)) = 0

Combine like terms: 3x + 2x = 5x
7(-6 + 5x + -1x2) = 0
(-6 * 7 + 5x * 7 + -1x2 * 7) = 0
(-42 + 35x + -7x2) = 0

Solving
-42 + 35x + -7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + 5x + -1x2) = 0

Factor a trinomial.
7((-3 + x)(2 + -1x)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {3, 2}

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