5x(x+1)=x+12

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Solution for 5x(x+1)=x+12 equation:


Simplifying
5x(x + 1) = x + 12

Reorder the terms:
5x(1 + x) = x + 12
(1 * 5x + x * 5x) = x + 12
(5x + 5x2) = x + 12

Reorder the terms:
5x + 5x2 = 12 + x

Solving
5x + 5x2 = 12 + x

Solving for variable 'x'.

Reorder the terms:
-12 + 5x + -1x + 5x2 = 12 + x + -12 + -1x

Combine like terms: 5x + -1x = 4x
-12 + 4x + 5x2 = 12 + x + -12 + -1x

Reorder the terms:
-12 + 4x + 5x2 = 12 + -12 + x + -1x

Combine like terms: 12 + -12 = 0
-12 + 4x + 5x2 = 0 + x + -1x
-12 + 4x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + 4x + 5x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -5x) = 0

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 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 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2

Solution

x = {-2, 1.2}

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