(10x+12)(x+40)*.5=0

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Solution for (10x+12)(x+40)*.5=0 equation: 


Simplifying
(10x + 12)(x + 40) * 0.5 = 0

Reorder the terms:
(12 + 10x)(x + 40) * 0.5 = 0

Reorder the terms:
(12 + 10x)(40 + x) * 0.5 = 0

Reorder the terms for easier multiplication:
0.5(12 + 10x)(40 + x) = 0

Multiply (12 + 10x) * (40 + x)
0.5(12(40 + x) + 10x * (40 + x)) = 0
0.5((40 * 12 + x * 12) + 10x * (40 + x)) = 0
0.5((480 + 12x) + 10x * (40 + x)) = 0
0.5(480 + 12x + (40 * 10x + x * 10x)) = 0
0.5(480 + 12x + (400x + 10x2)) = 0

Combine like terms: 12x + 400x = 412x
0.5(480 + 412x + 10x2) = 0
(480 * 0.5 + 412x * 0.5 + 10x2 * 0.5) = 0
(240 + 206x + 5x2) = 0

Solving
240 + 206x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(40 + x)(6 + 5x) = 0


Subproblem 1
Set the factor '(40 + x)' equal to zero and attempt to solve:

Simplifying
40 + x = 0

Solving
40 + x = 0

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

Add '-40' to each side of the equation.
40 + -40 + x = 0 + -40

Combine like terms: 40 + -40 = 0
0 + x = 0 + -40
x = 0 + -40

Combine like terms: 0 + -40 = -40
x = -40

Simplifying
x = -40

Subproblem 2
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 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 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Solution
x = {-40, -1.2}

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