(X+3)(X+2)=90

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Solution for (X+3)(X+2)=90 equation:


Simplifying
(X + 3)(X + 2) = 90

Reorder the terms:
(3 + X)(X + 2) = 90

Reorder the terms:
(3 + X)(2 + X) = 90

Multiply (3 + X) * (2 + X)
(3(2 + X) + X(2 + X)) = 90
((2 * 3 + X * 3) + X(2 + X)) = 90
((6 + 3X) + X(2 + X)) = 90
(6 + 3X + (2 * X + X * X)) = 90
(6 + 3X + (2X + X2)) = 90

Combine like terms: 3X + 2X = 5X
(6 + 5X + X2) = 90

Solving
6 + 5X + X2 = 90

Solving for variable 'X'.

Reorder the terms:
6 + -90 + 5X + X2 = 90 + -90

Combine like terms: 6 + -90 = -84
-84 + 5X + X2 = 90 + -90

Combine like terms: 90 + -90 = 0
-84 + 5X + X2 = 0

Factor a trinomial.
(-12 + -1X)(7 + -1X) = 0

Subproblem 1

Set the factor '(-12 + -1X)' equal to zero and attempt to solve: Simplifying -12 + -1X = 0 Solving -12 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1X = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1X = 0 + 12 -1X = 0 + 12 Combine like terms: 0 + 12 = 12 -1X = 12 Divide each side by '-1'. X = -12 Simplifying X = -12

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 = {-12, 7}

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