(3x+5)(x-3)=5

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Solution for (3x+5)(x-3)=5 equation:


Simplifying
(3x + 5)(x + -3) = 5

Reorder the terms:
(5 + 3x)(x + -3) = 5

Reorder the terms:
(5 + 3x)(-3 + x) = 5

Multiply (5 + 3x) * (-3 + x)
(5(-3 + x) + 3x * (-3 + x)) = 5
((-3 * 5 + x * 5) + 3x * (-3 + x)) = 5
((-15 + 5x) + 3x * (-3 + x)) = 5
(-15 + 5x + (-3 * 3x + x * 3x)) = 5
(-15 + 5x + (-9x + 3x2)) = 5

Combine like terms: 5x + -9x = -4x
(-15 + -4x + 3x2) = 5

Solving
-15 + -4x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
-15 + -5 + -4x + 3x2 = 5 + -5

Combine like terms: -15 + -5 = -20
-20 + -4x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-20 + -4x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(10 + -3x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Divide each side by '-3'. x = 3.333333333 Simplifying x = 3.333333333

Solution

x = {-2, 3.333333333}

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