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Simplifying x(5x + 4) = 2x2 + -3x + 6 Reorder the terms: x(4 + 5x) = 2x2 + -3x + 6 (4 * x + 5x * x) = 2x2 + -3x + 6 (4x + 5x2) = 2x2 + -3x + 6 Reorder the terms: 4x + 5x2 = 6 + -3x + 2x2 Solving 4x + 5x2 = 6 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -6 + 4x + 3x + 5x2 + -2x2 = 6 + -3x + 2x2 + -6 + 3x + -2x2 Combine like terms: 4x + 3x = 7x -6 + 7x + 5x2 + -2x2 = 6 + -3x + 2x2 + -6 + 3x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -6 + 7x + 3x2 = 6 + -3x + 2x2 + -6 + 3x + -2x2 Reorder the terms: -6 + 7x + 3x2 = 6 + -6 + -3x + 3x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 -6 + 7x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2 -6 + 7x + 3x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 -6 + 7x + 3x2 = 0 + 2x2 + -2x2 -6 + 7x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + 7x + 3x2 = 0 Factor a trinomial. (-3 + -1x)(2 + -3x) = 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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-3, 0.6666666667}
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