4x^2-9x-3=2x-9

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Solution for 4x^2-9x-3=2x-9 equation:


Simplifying
4x2 + -9x + -3 = 2x + -9

Reorder the terms:
-3 + -9x + 4x2 = 2x + -9

Reorder the terms:
-3 + -9x + 4x2 = -9 + 2x

Solving
-3 + -9x + 4x2 = -9 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + 9 + -9x + -2x + 4x2 = -9 + 2x + 9 + -2x

Combine like terms: -3 + 9 = 6
6 + -9x + -2x + 4x2 = -9 + 2x + 9 + -2x

Combine like terms: -9x + -2x = -11x
6 + -11x + 4x2 = -9 + 2x + 9 + -2x

Reorder the terms:
6 + -11x + 4x2 = -9 + 9 + 2x + -2x

Combine like terms: -9 + 9 = 0
6 + -11x + 4x2 = 0 + 2x + -2x
6 + -11x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -11x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(2 + -1x) = 0

Subproblem 1

Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75

Subproblem 2

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

Solution

x = {0.75, 2}

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