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Simplifying 3x(2x + -1) + 2(x + -1)(3x + -5) = 20 Reorder the terms: 3x(-1 + 2x) + 2(x + -1)(3x + -5) = 20 (-1 * 3x + 2x * 3x) + 2(x + -1)(3x + -5) = 20 (-3x + 6x2) + 2(x + -1)(3x + -5) = 20 Reorder the terms: -3x + 6x2 + 2(-1 + x)(3x + -5) = 20 Reorder the terms: -3x + 6x2 + 2(-1 + x)(-5 + 3x) = 20 Multiply (-1 + x) * (-5 + 3x) -3x + 6x2 + 2(-1(-5 + 3x) + x(-5 + 3x)) = 20 -3x + 6x2 + 2((-5 * -1 + 3x * -1) + x(-5 + 3x)) = 20 -3x + 6x2 + 2((5 + -3x) + x(-5 + 3x)) = 20 -3x + 6x2 + 2(5 + -3x + (-5 * x + 3x * x)) = 20 -3x + 6x2 + 2(5 + -3x + (-5x + 3x2)) = 20 Combine like terms: -3x + -5x = -8x -3x + 6x2 + 2(5 + -8x + 3x2) = 20 -3x + 6x2 + (5 * 2 + -8x * 2 + 3x2 * 2) = 20 -3x + 6x2 + (10 + -16x + 6x2) = 20 Reorder the terms: 10 + -3x + -16x + 6x2 + 6x2 = 20 Combine like terms: -3x + -16x = -19x 10 + -19x + 6x2 + 6x2 = 20 Combine like terms: 6x2 + 6x2 = 12x2 10 + -19x + 12x2 = 20 Solving 10 + -19x + 12x2 = 20 Solving for variable 'x'. Reorder the terms: 10 + -20 + -19x + 12x2 = 20 + -20 Combine like terms: 10 + -20 = -10 -10 + -19x + 12x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -10 + -19x + 12x2 = 0 Factor a trinomial. (-5 + -12x)(2 + -1x) = 0Subproblem 1
Set the factor '(-5 + -12x)' equal to zero and attempt to solve: Simplifying -5 + -12x = 0 Solving -5 + -12x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -12x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -12x = 0 + 5 -12x = 0 + 5 Combine like terms: 0 + 5 = 5 -12x = 5 Divide each side by '-12'. x = -0.4166666667 Simplifying x = -0.4166666667Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-0.4166666667, 2}
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