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Simplifying (5x + -2)(10x + -3) + -1(5x + -2)(7x + 3) = 0 Reorder the terms: (-2 + 5x)(10x + -3) + -1(5x + -2)(7x + 3) = 0 Reorder the terms: (-2 + 5x)(-3 + 10x) + -1(5x + -2)(7x + 3) = 0 Multiply (-2 + 5x) * (-3 + 10x) (-2(-3 + 10x) + 5x * (-3 + 10x)) + -1(5x + -2)(7x + 3) = 0 ((-3 * -2 + 10x * -2) + 5x * (-3 + 10x)) + -1(5x + -2)(7x + 3) = 0 ((6 + -20x) + 5x * (-3 + 10x)) + -1(5x + -2)(7x + 3) = 0 (6 + -20x + (-3 * 5x + 10x * 5x)) + -1(5x + -2)(7x + 3) = 0 (6 + -20x + (-15x + 50x2)) + -1(5x + -2)(7x + 3) = 0 Combine like terms: -20x + -15x = -35x (6 + -35x + 50x2) + -1(5x + -2)(7x + 3) = 0 Reorder the terms: 6 + -35x + 50x2 + -1(-2 + 5x)(7x + 3) = 0 Reorder the terms: 6 + -35x + 50x2 + -1(-2 + 5x)(3 + 7x) = 0 Multiply (-2 + 5x) * (3 + 7x) 6 + -35x + 50x2 + -1(-2(3 + 7x) + 5x * (3 + 7x)) = 0 6 + -35x + 50x2 + -1((3 * -2 + 7x * -2) + 5x * (3 + 7x)) = 0 6 + -35x + 50x2 + -1((-6 + -14x) + 5x * (3 + 7x)) = 0 6 + -35x + 50x2 + -1(-6 + -14x + (3 * 5x + 7x * 5x)) = 0 6 + -35x + 50x2 + -1(-6 + -14x + (15x + 35x2)) = 0 Combine like terms: -14x + 15x = 1x 6 + -35x + 50x2 + -1(-6 + 1x + 35x2) = 0 6 + -35x + 50x2 + (-6 * -1 + 1x * -1 + 35x2 * -1) = 0 6 + -35x + 50x2 + (6 + -1x + -35x2) = 0 Reorder the terms: 6 + 6 + -35x + -1x + 50x2 + -35x2 = 0 Combine like terms: 6 + 6 = 12 12 + -35x + -1x + 50x2 + -35x2 = 0 Combine like terms: -35x + -1x = -36x 12 + -36x + 50x2 + -35x2 = 0 Combine like terms: 50x2 + -35x2 = 15x2 12 + -36x + 15x2 = 0 Solving 12 + -36x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -12x + 5x2) = 0 Factor a trinomial. 3((2 + -5x)(2 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = 0.4Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0.4, 2}
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