(3x+90)*(6x-3)=0

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Solution for (3x+90)*(6x-3)=0 equation: 


Simplifying
(3x + 90)(6x + -3) = 0

Reorder the terms:
(90 + 3x)(6x + -3) = 0

Reorder the terms:
(90 + 3x)(-3 + 6x) = 0

Multiply (90 + 3x) * (-3 + 6x)
(90(-3 + 6x) + 3x * (-3 + 6x)) = 0
((-3 * 90 + 6x * 90) + 3x * (-3 + 6x)) = 0
((-270 + 540x) + 3x * (-3 + 6x)) = 0
(-270 + 540x + (-3 * 3x + 6x * 3x)) = 0
(-270 + 540x + (-9x + 18x2)) = 0

Combine like terms: 540x + -9x = 531x
(-270 + 531x + 18x2) = 0

Solving
-270 + 531x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-30 + 59x + 2x2) = 0

Factor a trinomial.
9((-30 + -1x)(1 + -2x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve:

Simplifying
-30 + -1x = 0

Solving
-30 + -1x = 0

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

Add '30' to each side of the equation.
-30 + 30 + -1x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1x = 0 + 30
-1x = 0 + 30

Combine like terms: 0 + 30 = 30
-1x = 30

Divide each side by '-1'.
x = -30

Simplifying
x = -30

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-30, 0.5}

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