(3x+2)(x-5)=28

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Solution for (3x+2)(x-5)=28 equation: 


Simplifying
(3x + 2)(x + -5) = 28

Reorder the terms:
(2 + 3x)(x + -5) = 28

Reorder the terms:
(2 + 3x)(-5 + x) = 28

Multiply (2 + 3x) * (-5 + x)
(2(-5 + x) + 3x * (-5 + x)) = 28
((-5 * 2 + x * 2) + 3x * (-5 + x)) = 28
((-10 + 2x) + 3x * (-5 + x)) = 28
(-10 + 2x + (-5 * 3x + x * 3x)) = 28
(-10 + 2x + (-15x + 3x2)) = 28

Combine like terms: 2x + -15x = -13x
(-10 + -13x + 3x2) = 28

Solving
-10 + -13x + 3x2 = 28

Solving for variable 'x'.

Reorder the terms:
-10 + -28 + -13x + 3x2 = 28 + -28

Combine like terms: -10 + -28 = -38
-38 + -13x + 3x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-38 + -13x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(19 + -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 '(19 + -3x)' equal to zero and attempt to solve:

Simplifying
19 + -3x = 0

Solving
19 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-19' to each side of the equation.
19 + -19 + -3x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -3x = 0 + -19
-3x = 0 + -19

Combine like terms: 0 + -19 = -19
-3x = -19

Divide each side by '-3'.
x = 6.333333333

Simplifying
x = 6.333333333
Solution
x = {-2, 6.333333333}

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