(3+2x)(x)=77

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Solution for (3+2x)(x)=77 equation:


Simplifying
(3 + 2x)(x) = 77

Reorder the terms for easier multiplication:
x(3 + 2x) = 77
(3 * x + 2x * x) = 77
(3x + 2x2) = 77

Solving
3x + 2x2 = 77

Solving for variable 'x'.

Reorder the terms:
-77 + 3x + 2x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 3x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(11 + -2x) = 0

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(11 + -2x)' equal to zero and attempt to solve: Simplifying 11 + -2x = 0 Solving 11 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2x = 0 + -11 -2x = 0 + -11 Combine like terms: 0 + -11 = -11 -2x = -11 Divide each side by '-2'. x = 5.5 Simplifying x = 5.5

Solution

x = {-7, 5.5}

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