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Simplifying x2 + -4 + (x + -2)(2x + -1) = (3x + 1)(5x + -4) Reorder the terms: x2 + -4 + (-2 + x)(2x + -1) = (3x + 1)(5x + -4) Reorder the terms: x2 + -4 + (-2 + x)(-1 + 2x) = (3x + 1)(5x + -4) Multiply (-2 + x) * (-1 + 2x) x2 + -4 + (-2(-1 + 2x) + x(-1 + 2x)) = (3x + 1)(5x + -4) x2 + -4 + ((-1 * -2 + 2x * -2) + x(-1 + 2x)) = (3x + 1)(5x + -4) x2 + -4 + ((2 + -4x) + x(-1 + 2x)) = (3x + 1)(5x + -4) x2 + -4 + (2 + -4x + (-1 * x + 2x * x)) = (3x + 1)(5x + -4) x2 + -4 + (2 + -4x + (-1x + 2x2)) = (3x + 1)(5x + -4) Combine like terms: -4x + -1x = -5x x2 + -4 + (2 + -5x + 2x2) = (3x + 1)(5x + -4) Reorder the terms: -4 + 2 + -5x + x2 + 2x2 = (3x + 1)(5x + -4) Combine like terms: -4 + 2 = -2 -2 + -5x + x2 + 2x2 = (3x + 1)(5x + -4) Combine like terms: x2 + 2x2 = 3x2 -2 + -5x + 3x2 = (3x + 1)(5x + -4) Reorder the terms: -2 + -5x + 3x2 = (1 + 3x)(5x + -4) Reorder the terms: -2 + -5x + 3x2 = (1 + 3x)(-4 + 5x) Multiply (1 + 3x) * (-4 + 5x) -2 + -5x + 3x2 = (1(-4 + 5x) + 3x * (-4 + 5x)) -2 + -5x + 3x2 = ((-4 * 1 + 5x * 1) + 3x * (-4 + 5x)) -2 + -5x + 3x2 = ((-4 + 5x) + 3x * (-4 + 5x)) -2 + -5x + 3x2 = (-4 + 5x + (-4 * 3x + 5x * 3x)) -2 + -5x + 3x2 = (-4 + 5x + (-12x + 15x2)) Combine like terms: 5x + -12x = -7x -2 + -5x + 3x2 = (-4 + -7x + 15x2) Solving -2 + -5x + 3x2 = -4 + -7x + 15x2 Solving for variable 'x'. Reorder the terms: -2 + 4 + -5x + 7x + 3x2 + -15x2 = -4 + -7x + 15x2 + 4 + 7x + -15x2 Combine like terms: -2 + 4 = 2 2 + -5x + 7x + 3x2 + -15x2 = -4 + -7x + 15x2 + 4 + 7x + -15x2 Combine like terms: -5x + 7x = 2x 2 + 2x + 3x2 + -15x2 = -4 + -7x + 15x2 + 4 + 7x + -15x2 Combine like terms: 3x2 + -15x2 = -12x2 2 + 2x + -12x2 = -4 + -7x + 15x2 + 4 + 7x + -15x2 Reorder the terms: 2 + 2x + -12x2 = -4 + 4 + -7x + 7x + 15x2 + -15x2 Combine like terms: -4 + 4 = 0 2 + 2x + -12x2 = 0 + -7x + 7x + 15x2 + -15x2 2 + 2x + -12x2 = -7x + 7x + 15x2 + -15x2 Combine like terms: -7x + 7x = 0 2 + 2x + -12x2 = 0 + 15x2 + -15x2 2 + 2x + -12x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 2 + 2x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + x + -6x2) = 0 Factor a trinomial. 2((1 + -2x)(1 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0.5, -0.3333333333}
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