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Simplifying 6x2 + 5x + 15 = 2x2 + -3x + 12 Reorder the terms: 15 + 5x + 6x2 = 2x2 + -3x + 12 Reorder the terms: 15 + 5x + 6x2 = 12 + -3x + 2x2 Solving 15 + 5x + 6x2 = 12 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: 15 + -12 + 5x + 3x + 6x2 + -2x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2 Combine like terms: 15 + -12 = 3 3 + 5x + 3x + 6x2 + -2x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2 Combine like terms: 5x + 3x = 8x 3 + 8x + 6x2 + -2x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 3 + 8x + 4x2 = 12 + -3x + 2x2 + -12 + 3x + -2x2 Reorder the terms: 3 + 8x + 4x2 = 12 + -12 + -3x + 3x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 3 + 8x + 4x2 = 0 + -3x + 3x + 2x2 + -2x2 3 + 8x + 4x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 3 + 8x + 4x2 = 0 + 2x2 + -2x2 3 + 8x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 3 + 8x + 4x2 = 0 Factor a trinomial. (3 + 2x)(1 + 2x) = 0Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, -0.5}
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