(1-x)*(2-x)=30

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Solution for (1-x)*(2-x)=30 equation:


Simplifying
(1 + -1x)(2 + -1x) = 30

Multiply (1 + -1x) * (2 + -1x)
(1(2 + -1x) + -1x * (2 + -1x)) = 30
((2 * 1 + -1x * 1) + -1x * (2 + -1x)) = 30
((2 + -1x) + -1x * (2 + -1x)) = 30
(2 + -1x + (2 * -1x + -1x * -1x)) = 30
(2 + -1x + (-2x + 1x2)) = 30

Combine like terms: -1x + -2x = -3x
(2 + -3x + 1x2) = 30

Solving
2 + -3x + 1x2 = 30

Solving for variable 'x'.

Reorder the terms:
2 + -30 + -3x + 1x2 = 30 + -30

Combine like terms: 2 + -30 = -28
-28 + -3x + 1x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-28 + -3x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -1x) = 0

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

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 = {-4, 7}

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