x^2=4(x+120)

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Solution for x^2=4(x+120) equation: 


Simplifying
x2 = 4(x + 120)

Reorder the terms:
x2 = 4(120 + x)
x2 = (120 * 4 + x * 4)
x2 = (480 + 4x)

Solving
x2 = 480 + 4x

Solving for variable 'x'.

Reorder the terms:
-480 + -4x + x2 = 480 + 4x + -480 + -4x

Reorder the terms:
-480 + -4x + x2 = 480 + -480 + 4x + -4x

Combine like terms: 480 + -480 = 0
-480 + -4x + x2 = 0 + 4x + -4x
-480 + -4x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-480 + -4x + x2 = 0

Factor a trinomial.
(-20 + -1x)(24 + -1x) = 0


Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20

Subproblem 2
Set the factor '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1x = 0 + -24
-1x = 0 + -24

Combine like terms: 0 + -24 = -24
-1x = -24

Divide each side by '-1'.
x = 24

Simplifying
x = 24
Solution
x = {-20, 24}

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