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Simplifying 3(2x + -1)(5x + 2) = 2(15x + 6)(6x + -1) Reorder the terms: 3(-1 + 2x)(5x + 2) = 2(15x + 6)(6x + -1) Reorder the terms: 3(-1 + 2x)(2 + 5x) = 2(15x + 6)(6x + -1) Multiply (-1 + 2x) * (2 + 5x) 3(-1(2 + 5x) + 2x * (2 + 5x)) = 2(15x + 6)(6x + -1) 3((2 * -1 + 5x * -1) + 2x * (2 + 5x)) = 2(15x + 6)(6x + -1) 3((-2 + -5x) + 2x * (2 + 5x)) = 2(15x + 6)(6x + -1) 3(-2 + -5x + (2 * 2x + 5x * 2x)) = 2(15x + 6)(6x + -1) 3(-2 + -5x + (4x + 10x2)) = 2(15x + 6)(6x + -1) Combine like terms: -5x + 4x = -1x 3(-2 + -1x + 10x2) = 2(15x + 6)(6x + -1) (-2 * 3 + -1x * 3 + 10x2 * 3) = 2(15x + 6)(6x + -1) (-6 + -3x + 30x2) = 2(15x + 6)(6x + -1) Reorder the terms: -6 + -3x + 30x2 = 2(6 + 15x)(6x + -1) Reorder the terms: -6 + -3x + 30x2 = 2(6 + 15x)(-1 + 6x) Multiply (6 + 15x) * (-1 + 6x) -6 + -3x + 30x2 = 2(6(-1 + 6x) + 15x * (-1 + 6x)) -6 + -3x + 30x2 = 2((-1 * 6 + 6x * 6) + 15x * (-1 + 6x)) -6 + -3x + 30x2 = 2((-6 + 36x) + 15x * (-1 + 6x)) -6 + -3x + 30x2 = 2(-6 + 36x + (-1 * 15x + 6x * 15x)) -6 + -3x + 30x2 = 2(-6 + 36x + (-15x + 90x2)) Combine like terms: 36x + -15x = 21x -6 + -3x + 30x2 = 2(-6 + 21x + 90x2) -6 + -3x + 30x2 = (-6 * 2 + 21x * 2 + 90x2 * 2) -6 + -3x + 30x2 = (-12 + 42x + 180x2) Solving -6 + -3x + 30x2 = -12 + 42x + 180x2 Solving for variable 'x'. Reorder the terms: -6 + 12 + -3x + -42x + 30x2 + -180x2 = -12 + 42x + 180x2 + 12 + -42x + -180x2 Combine like terms: -6 + 12 = 6 6 + -3x + -42x + 30x2 + -180x2 = -12 + 42x + 180x2 + 12 + -42x + -180x2 Combine like terms: -3x + -42x = -45x 6 + -45x + 30x2 + -180x2 = -12 + 42x + 180x2 + 12 + -42x + -180x2 Combine like terms: 30x2 + -180x2 = -150x2 6 + -45x + -150x2 = -12 + 42x + 180x2 + 12 + -42x + -180x2 Reorder the terms: 6 + -45x + -150x2 = -12 + 12 + 42x + -42x + 180x2 + -180x2 Combine like terms: -12 + 12 = 0 6 + -45x + -150x2 = 0 + 42x + -42x + 180x2 + -180x2 6 + -45x + -150x2 = 42x + -42x + 180x2 + -180x2 Combine like terms: 42x + -42x = 0 6 + -45x + -150x2 = 0 + 180x2 + -180x2 6 + -45x + -150x2 = 180x2 + -180x2 Combine like terms: 180x2 + -180x2 = 0 6 + -45x + -150x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -15x + -50x2) = 0 Factor a trinomial. 3((1 + -10x)(2 + 5x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -10x)' equal to zero and attempt to solve: Simplifying 1 + -10x = 0 Solving 1 + -10x = 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 + -10x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10x = 0 + -1 -10x = 0 + -1 Combine like terms: 0 + -1 = -1 -10x = -1 Divide each side by '-10'. x = 0.1 Simplifying x = 0.1Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 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 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4Solution
x = {0.1, -0.4}
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