(x+3)(2x-4)=28

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Solution for (x+3)(2x-4)=28 equation: 


Simplifying
(x + 3)(2x + -4) = 28

Reorder the terms:
(3 + x)(2x + -4) = 28

Reorder the terms:
(3 + x)(-4 + 2x) = 28

Multiply (3 + x) * (-4 + 2x)
(3(-4 + 2x) + x(-4 + 2x)) = 28
((-4 * 3 + 2x * 3) + x(-4 + 2x)) = 28
((-12 + 6x) + x(-4 + 2x)) = 28
(-12 + 6x + (-4 * x + 2x * x)) = 28
(-12 + 6x + (-4x + 2x2)) = 28

Combine like terms: 6x + -4x = 2x
(-12 + 2x + 2x2) = 28

Solving
-12 + 2x + 2x2 = 28

Solving for variable 'x'.

Reorder the terms:
-12 + -28 + 2x + 2x2 = 28 + -28

Combine like terms: -12 + -28 = -40
-40 + 2x + 2x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-40 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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