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Simplifying 5x2 + 2x + 12 = 4x2 + 15x + -18 Reorder the terms: 12 + 2x + 5x2 = 4x2 + 15x + -18 Reorder the terms: 12 + 2x + 5x2 = -18 + 15x + 4x2 Solving 12 + 2x + 5x2 = -18 + 15x + 4x2 Solving for variable 'x'. Reorder the terms: 12 + 18 + 2x + -15x + 5x2 + -4x2 = -18 + 15x + 4x2 + 18 + -15x + -4x2 Combine like terms: 12 + 18 = 30 30 + 2x + -15x + 5x2 + -4x2 = -18 + 15x + 4x2 + 18 + -15x + -4x2 Combine like terms: 2x + -15x = -13x 30 + -13x + 5x2 + -4x2 = -18 + 15x + 4x2 + 18 + -15x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 30 + -13x + 1x2 = -18 + 15x + 4x2 + 18 + -15x + -4x2 Reorder the terms: 30 + -13x + 1x2 = -18 + 18 + 15x + -15x + 4x2 + -4x2 Combine like terms: -18 + 18 = 0 30 + -13x + 1x2 = 0 + 15x + -15x + 4x2 + -4x2 30 + -13x + 1x2 = 15x + -15x + 4x2 + -4x2 Combine like terms: 15x + -15x = 0 30 + -13x + 1x2 = 0 + 4x2 + -4x2 30 + -13x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 30 + -13x + 1x2 = 0 Factor a trinomial. (3 + -1x)(10 + -1x) = 0Subproblem 1
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 = 3Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {3, 10}
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