(x-3)(x+2)=50

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Solution for (x-3)(x+2)=50 equation:


Simplifying
(x + -3)(x + 2) = 50

Reorder the terms:
(-3 + x)(x + 2) = 50

Reorder the terms:
(-3 + x)(2 + x) = 50

Multiply (-3 + x) * (2 + x)
(-3(2 + x) + x(2 + x)) = 50
((2 * -3 + x * -3) + x(2 + x)) = 50
((-6 + -3x) + x(2 + x)) = 50
(-6 + -3x + (2 * x + x * x)) = 50
(-6 + -3x + (2x + x2)) = 50

Combine like terms: -3x + 2x = -1x
(-6 + -1x + x2) = 50

Solving
-6 + -1x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
-6 + -50 + -1x + x2 = 50 + -50

Combine like terms: -6 + -50 = -56
-56 + -1x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-56 + -1x + x2 = 0

Factor a trinomial.
(-7 + -1x)(8 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-7, 8}

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