2x^2+5x+3=12x

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Solution for 2x^2+5x+3=12x equation:


Simplifying
2x2 + 5x + 3 = 12x

Reorder the terms:
3 + 5x + 2x2 = 12x

Solving
3 + 5x + 2x2 = 12x

Solving for variable 'x'.

Reorder the terms:
3 + 5x + -12x + 2x2 = 12x + -12x

Combine like terms: 5x + -12x = -7x
3 + -7x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
3 + -7x + 2x2 = 0

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

Subproblem 1

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0.5, 3}

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