(x-3)(2x+5)=6

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Solution for (x-3)(2x+5)=6 equation:


Simplifying
(x + -3)(2x + 5) = 6

Reorder the terms:
(-3 + x)(2x + 5) = 6

Reorder the terms:
(-3 + x)(5 + 2x) = 6

Multiply (-3 + x) * (5 + 2x)
(-3(5 + 2x) + x(5 + 2x)) = 6
((5 * -3 + 2x * -3) + x(5 + 2x)) = 6
((-15 + -6x) + x(5 + 2x)) = 6
(-15 + -6x + (5 * x + 2x * x)) = 6
(-15 + -6x + (5x + 2x2)) = 6

Combine like terms: -6x + 5x = -1x
(-15 + -1x + 2x2) = 6

Solving
-15 + -1x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-15 + -6 + -1x + 2x2 = 6 + -6

Combine like terms: -15 + -6 = -21
-21 + -1x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-21 + -1x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -2x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5

Solution

x = {-3, 3.5}

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