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Simplifying 5x + 3 = 12x + -4x2 Reorder the terms: 3 + 5x = 12x + -4x2 Solving 3 + 5x = 12x + -4x2 Solving for variable 'x'. Combine like terms: 5x + -12x = -7x 3 + -7x + 4x2 = 12x + -4x2 + -12x + 4x2 Reorder the terms: 3 + -7x + 4x2 = 12x + -12x + -4x2 + 4x2 Combine like terms: 12x + -12x = 0 3 + -7x + 4x2 = 0 + -4x2 + 4x2 3 + -7x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 3 + -7x + 4x2 = 0 Factor a trinomial. (3 + -4x)(1 + -1x) = 0Subproblem 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 = 0.75Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.75, 1}
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