3x(2x-1)=30

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Solution for 3x(2x-1)=30 equation:


Simplifying
3x(2x + -1) = 30

Reorder the terms:
3x(-1 + 2x) = 30
(-1 * 3x + 2x * 3x) = 30
(-3x + 6x2) = 30

Solving
-3x + 6x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + -3x + 6x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -3x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -1x + 2x2) = 0

Factor a trinomial.
3((-2 + -1x)(5 + -2x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-2, 2.5}

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