(x-3)(2x+4)=600

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Solution for (x-3)(2x+4)=600 equation: 


Simplifying
(x + -3)(2x + 4) = 600

Reorder the terms:
(-3 + x)(2x + 4) = 600

Reorder the terms:
(-3 + x)(4 + 2x) = 600

Multiply (-3 + x) * (4 + 2x)
(-3(4 + 2x) + x(4 + 2x)) = 600
((4 * -3 + 2x * -3) + x(4 + 2x)) = 600
((-12 + -6x) + x(4 + 2x)) = 600
(-12 + -6x + (4 * x + 2x * x)) = 600
(-12 + -6x + (4x + 2x2)) = 600

Combine like terms: -6x + 4x = -2x
(-12 + -2x + 2x2) = 600

Solving
-12 + -2x + 2x2 = 600

Solving for variable 'x'.

Reorder the terms:
-12 + -600 + -2x + 2x2 = 600 + -600

Combine like terms: -12 + -600 = -612
-612 + -2x + 2x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-612 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-306 + -1x + x2) = 0

Factor a trinomial.
2((-17 + -1x)(18 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17

Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {-17, 18}

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