(2x+3)(x-5)=15

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Solution for (2x+3)(x-5)=15 equation:


Simplifying
(2x + 3)(x + -5) = 15

Reorder the terms:
(3 + 2x)(x + -5) = 15

Reorder the terms:
(3 + 2x)(-5 + x) = 15

Multiply (3 + 2x) * (-5 + x)
(3(-5 + x) + 2x * (-5 + x)) = 15
((-5 * 3 + x * 3) + 2x * (-5 + x)) = 15
((-15 + 3x) + 2x * (-5 + x)) = 15
(-15 + 3x + (-5 * 2x + x * 2x)) = 15
(-15 + 3x + (-10x + 2x2)) = 15

Combine like terms: 3x + -10x = -7x
(-15 + -7x + 2x2) = 15

Solving
-15 + -7x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -15 + -7x + 2x2 = 15 + -15

Combine like terms: -15 + -15 = -30
-30 + -7x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-30 + -7x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-2.5, 6}

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