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Simplifying (4 + -1x)(3x + -1) = 4 + -1x Reorder the terms: (4 + -1x)(-1 + 3x) = 4 + -1x Multiply (4 + -1x) * (-1 + 3x) (4(-1 + 3x) + -1x * (-1 + 3x)) = 4 + -1x ((-1 * 4 + 3x * 4) + -1x * (-1 + 3x)) = 4 + -1x ((-4 + 12x) + -1x * (-1 + 3x)) = 4 + -1x (-4 + 12x + (-1 * -1x + 3x * -1x)) = 4 + -1x (-4 + 12x + (1x + -3x2)) = 4 + -1x Combine like terms: 12x + 1x = 13x (-4 + 13x + -3x2) = 4 + -1x Solving -4 + 13x + -3x2 = 4 + -1x Solving for variable 'x'. Reorder the terms: -4 + -4 + 13x + x + -3x2 = 4 + -1x + -4 + x Combine like terms: -4 + -4 = -8 -8 + 13x + x + -3x2 = 4 + -1x + -4 + x Combine like terms: 13x + x = 14x -8 + 14x + -3x2 = 4 + -1x + -4 + x Reorder the terms: -8 + 14x + -3x2 = 4 + -4 + -1x + x Combine like terms: 4 + -4 = 0 -8 + 14x + -3x2 = 0 + -1x + x -8 + 14x + -3x2 = -1x + x Combine like terms: -1x + x = 0 -8 + 14x + -3x2 = 0 Factor a trinomial. (-4 + x)(2 + -3x) = 0Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 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 = {4, 0.6666666667}
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