x(2x+5)=75

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Solution for x(2x+5)=75 equation:


Simplifying
x(2x + 5) = 75

Reorder the terms:
x(5 + 2x) = 75
(5 * x + 2x * x) = 75
(5x + 2x2) = 75

Solving
5x + 2x2 = 75

Solving for variable 'x'.

Reorder the terms:
-75 + 5x + 2x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + 5x + 2x2 = 0

Factor a trinomial.
(-15 + -2x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-15 + -2x)' equal to zero and attempt to solve: Simplifying -15 + -2x = 0 Solving -15 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2x = 0 + 15 -2x = 0 + 15 Combine like terms: 0 + 15 = 15 -2x = 15 Divide each side by '-2'. x = -7.5 Simplifying x = -7.5

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 = {-7.5, 5}

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