3x(2x-5)=75

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Solution for 3x(2x-5)=75 equation:


Simplifying
3x(2x + -5) = 75

Reorder the terms:
3x(-5 + 2x) = 75
(-5 * 3x + 2x * 3x) = 75
(-15x + 6x2) = 75

Solving
-15x + 6x2 = 75

Solving for variable 'x'.

Reorder the terms:
-75 + -15x + 6x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + -15x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + -5x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-2.5, 5}

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