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Simplifying (-10 + 6x) = 15 + (-5 + 3x)(5 + 12x) Remove parenthesis around (-10 + 6x) -10 + 6x = 15 + (-5 + 3x)(5 + 12x) Multiply (-5 + 3x) * (5 + 12x) -10 + 6x = 15 + (-5(5 + 12x) + 3x * (5 + 12x)) -10 + 6x = 15 + ((5 * -5 + 12x * -5) + 3x * (5 + 12x)) -10 + 6x = 15 + ((-25 + -60x) + 3x * (5 + 12x)) -10 + 6x = 15 + (-25 + -60x + (5 * 3x + 12x * 3x)) -10 + 6x = 15 + (-25 + -60x + (15x + 36x2)) Combine like terms: -60x + 15x = -45x -10 + 6x = 15 + (-25 + -45x + 36x2) Combine like terms: 15 + -25 = -10 -10 + 6x = -10 + -45x + 36x2 Add '10' to each side of the equation. -10 + 10 + 6x = -10 + -45x + 10 + 36x2 Combine like terms: -10 + 10 = 0 0 + 6x = -10 + -45x + 10 + 36x2 6x = -10 + -45x + 10 + 36x2 Reorder the terms: 6x = -10 + 10 + -45x + 36x2 Combine like terms: -10 + 10 = 0 6x = 0 + -45x + 36x2 6x = -45x + 36x2 Solving 6x = -45x + 36x2 Solving for variable 'x'. Combine like terms: 6x + 45x = 51x 51x + -36x2 = -45x + 36x2 + 45x + -36x2 Reorder the terms: 51x + -36x2 = -45x + 45x + 36x2 + -36x2 Combine like terms: -45x + 45x = 0 51x + -36x2 = 0 + 36x2 + -36x2 51x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 51x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(17 + -12x) = 0 Ignore the factor 3.Subproblem 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 '(17 + -12x)' equal to zero and attempt to solve: Simplifying 17 + -12x = 0 Solving 17 + -12x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -12x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -12x = 0 + -17 -12x = 0 + -17 Combine like terms: 0 + -17 = -17 -12x = -17 Divide each side by '-12'. x = 1.416666667 Simplifying x = 1.416666667Solution
x = {0, 1.416666667}
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