180=(x+3)*(2x+4)

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Solution for 180=(x+3)*(2x+4) equation: 


Simplifying
180 = (x + 3)(2x + 4)

Reorder the terms:
180 = (3 + x)(2x + 4)

Reorder the terms:
180 = (3 + x)(4 + 2x)

Multiply (3 + x) * (4 + 2x)
180 = (3(4 + 2x) + x(4 + 2x))
180 = ((4 * 3 + 2x * 3) + x(4 + 2x))
180 = ((12 + 6x) + x(4 + 2x))
180 = (12 + 6x + (4 * x + 2x * x))
180 = (12 + 6x + (4x + 2x2))

Combine like terms: 6x + 4x = 10x
180 = (12 + 10x + 2x2)

Solving
180 = 12 + 10x + 2x2

Solving for variable 'x'.

Combine like terms: 180 + -12 = 168
168 + -10x + -2x2 = 12 + 10x + 2x2 + -12 + -10x + -2x2

Reorder the terms:
168 + -10x + -2x2 = 12 + -12 + 10x + -10x + 2x2 + -2x2

Combine like terms: 12 + -12 = 0
168 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2
168 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
168 + -10x + -2x2 = 0 + 2x2 + -2x2
168 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
168 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(84 + -5x + -1x2) = 0

Factor a trinomial.
2((7 + -1x)(12 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {7, -12}

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