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Simplifying 4x2 + 6x = x2 + 5x + 30 Reorder the terms: 6x + 4x2 = x2 + 5x + 30 Reorder the terms: 6x + 4x2 = 30 + 5x + x2 Solving 6x + 4x2 = 30 + 5x + x2 Solving for variable 'x'. Reorder the terms: -30 + 6x + -5x + 4x2 + -1x2 = 30 + 5x + x2 + -30 + -5x + -1x2 Combine like terms: 6x + -5x = 1x -30 + 1x + 4x2 + -1x2 = 30 + 5x + x2 + -30 + -5x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -30 + 1x + 3x2 = 30 + 5x + x2 + -30 + -5x + -1x2 Reorder the terms: -30 + 1x + 3x2 = 30 + -30 + 5x + -5x + x2 + -1x2 Combine like terms: 30 + -30 = 0 -30 + 1x + 3x2 = 0 + 5x + -5x + x2 + -1x2 -30 + 1x + 3x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 -30 + 1x + 3x2 = 0 + x2 + -1x2 -30 + 1x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -30 + 1x + 3x2 = 0 Factor a trinomial. (-10 + -3x)(3 + -1x) = 0Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve: Simplifying -10 + -3x = 0 Solving -10 + -3x = 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 + -3x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3x = 0 + 10 -3x = 0 + 10 Combine like terms: 0 + 10 = 10 -3x = 10 Divide each side by '-3'. x = -3.333333333 Simplifying x = -3.333333333Subproblem 2
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 = 3Solution
x = {-3.333333333, 3}
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