2x(x-5)=12

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Solution for 2x(x-5)=12 equation:


Simplifying
2x(x + -5) = 12

Reorder the terms:
2x(-5 + x) = 12
(-5 * 2x + x * 2x) = 12
(-10x + 2x2) = 12

Solving
-10x + 2x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + -10x + 2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -5x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(6 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-1, 6}

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