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Simplifying (x + 1)(6x + -10) = 15 + (3x + -5)(12x + 5) Reorder the terms: (1 + x)(6x + -10) = 15 + (3x + -5)(12x + 5) Reorder the terms: (1 + x)(-10 + 6x) = 15 + (3x + -5)(12x + 5) Multiply (1 + x) * (-10 + 6x) (1(-10 + 6x) + x(-10 + 6x)) = 15 + (3x + -5)(12x + 5) ((-10 * 1 + 6x * 1) + x(-10 + 6x)) = 15 + (3x + -5)(12x + 5) ((-10 + 6x) + x(-10 + 6x)) = 15 + (3x + -5)(12x + 5) (-10 + 6x + (-10 * x + 6x * x)) = 15 + (3x + -5)(12x + 5) (-10 + 6x + (-10x + 6x2)) = 15 + (3x + -5)(12x + 5) Combine like terms: 6x + -10x = -4x (-10 + -4x + 6x2) = 15 + (3x + -5)(12x + 5) Reorder the terms: -10 + -4x + 6x2 = 15 + (-5 + 3x)(12x + 5) Reorder the terms: -10 + -4x + 6x2 = 15 + (-5 + 3x)(5 + 12x) Multiply (-5 + 3x) * (5 + 12x) -10 + -4x + 6x2 = 15 + (-5(5 + 12x) + 3x * (5 + 12x)) -10 + -4x + 6x2 = 15 + ((5 * -5 + 12x * -5) + 3x * (5 + 12x)) -10 + -4x + 6x2 = 15 + ((-25 + -60x) + 3x * (5 + 12x)) -10 + -4x + 6x2 = 15 + (-25 + -60x + (5 * 3x + 12x * 3x)) -10 + -4x + 6x2 = 15 + (-25 + -60x + (15x + 36x2)) Combine like terms: -60x + 15x = -45x -10 + -4x + 6x2 = 15 + (-25 + -45x + 36x2) Combine like terms: 15 + -25 = -10 -10 + -4x + 6x2 = -10 + -45x + 36x2 Add '10' to each side of the equation. -10 + -4x + 10 + 6x2 = -10 + -45x + 10 + 36x2 Reorder the terms: -10 + 10 + -4x + 6x2 = -10 + -45x + 10 + 36x2 Combine like terms: -10 + 10 = 0 0 + -4x + 6x2 = -10 + -45x + 10 + 36x2 -4x + 6x2 = -10 + -45x + 10 + 36x2 Reorder the terms: -4x + 6x2 = -10 + 10 + -45x + 36x2 Combine like terms: -10 + 10 = 0 -4x + 6x2 = 0 + -45x + 36x2 -4x + 6x2 = -45x + 36x2 Solving -4x + 6x2 = -45x + 36x2 Solving for variable 'x'. Reorder the terms: -4x + 45x + 6x2 + -36x2 = -45x + 36x2 + 45x + -36x2 Combine like terms: -4x + 45x = 41x 41x + 6x2 + -36x2 = -45x + 36x2 + 45x + -36x2 Combine like terms: 6x2 + -36x2 = -30x2 41x + -30x2 = -45x + 36x2 + 45x + -36x2 Reorder the terms: 41x + -30x2 = -45x + 45x + 36x2 + -36x2 Combine like terms: -45x + 45x = 0 41x + -30x2 = 0 + 36x2 + -36x2 41x + -30x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 41x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(41 + -30x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(41 + -30x)' equal to zero and attempt to solve: Simplifying 41 + -30x = 0 Solving 41 + -30x = 0 Move all terms containing x to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + -30x = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -30x = 0 + -41 -30x = 0 + -41 Combine like terms: 0 + -41 = -41 -30x = -41 Divide each side by '-30'. x = 1.366666667 Simplifying x = 1.366666667Solution
x = {0, 1.366666667}
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