30=5x^2-5x

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Solution for 30=5x^2-5x equation:


Simplifying
30 = 5x2 + -5x

Reorder the terms:
30 = -5x + 5x2

Solving
30 = -5x + 5x2

Solving for variable 'x'.

Reorder the terms:
30 + 5x + -5x2 = -5x + 5x + 5x2 + -5x2

Combine like terms: -5x + 5x = 0
30 + 5x + -5x2 = 0 + 5x2 + -5x2
30 + 5x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
30 + 5x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + x + -1x2) = 0

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

Ignore the factor 5.

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {3, -2}

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