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Simplifying 2x(3x + 2) = 5 + -6x2 Reorder the terms: 2x(2 + 3x) = 5 + -6x2 (2 * 2x + 3x * 2x) = 5 + -6x2 (4x + 6x2) = 5 + -6x2 Solving 4x + 6x2 = 5 + -6x2 Solving for variable 'x'. Reorder the terms: -5 + 4x + 6x2 + 6x2 = 5 + -6x2 + -5 + 6x2 Combine like terms: 6x2 + 6x2 = 12x2 -5 + 4x + 12x2 = 5 + -6x2 + -5 + 6x2 Reorder the terms: -5 + 4x + 12x2 = 5 + -5 + -6x2 + 6x2 Combine like terms: 5 + -5 = 0 -5 + 4x + 12x2 = 0 + -6x2 + 6x2 -5 + 4x + 12x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -5 + 4x + 12x2 = 0 Factor a trinomial. (-5 + -6x)(1 + -2x) = 0Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve: Simplifying -5 + -6x = 0 Solving -5 + -6x = 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 + -6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x = 0 + 5 -6x = 0 + 5 Combine like terms: 0 + 5 = 5 -6x = 5 Divide each side by '-6'. x = -0.8333333333 Simplifying x = -0.8333333333Subproblem 2
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 = 0.5Solution
x = {-0.8333333333, 0.5}
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