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Simplifying 15x + 10 = 4x2 + 12x + 9 Reorder the terms: 10 + 15x = 4x2 + 12x + 9 Reorder the terms: 10 + 15x = 9 + 12x + 4x2 Solving 10 + 15x = 9 + 12x + 4x2 Solving for variable 'x'. Reorder the terms: 10 + -9 + 15x + -12x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: 10 + -9 = 1 1 + 15x + -12x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: 15x + -12x = 3x 1 + 3x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Reorder the terms: 1 + 3x + -4x2 = 9 + -9 + 12x + -12x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 1 + 3x + -4x2 = 0 + 12x + -12x + 4x2 + -4x2 1 + 3x + -4x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 1 + 3x + -4x2 = 0 + 4x2 + -4x2 1 + 3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 1 + 3x + -4x2 = 0 Factor a trinomial. (1 + -1x)(1 + 4x) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {1, -0.25}
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