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Simplifying 8x(x + 1) + (5x + -1)(3x + 5) = 3(3x + 5)(x + 1) Reorder the terms: 8x(1 + x) + (5x + -1)(3x + 5) = 3(3x + 5)(x + 1) (1 * 8x + x * 8x) + (5x + -1)(3x + 5) = 3(3x + 5)(x + 1) (8x + 8x2) + (5x + -1)(3x + 5) = 3(3x + 5)(x + 1) Reorder the terms: 8x + 8x2 + (-1 + 5x)(3x + 5) = 3(3x + 5)(x + 1) Reorder the terms: 8x + 8x2 + (-1 + 5x)(5 + 3x) = 3(3x + 5)(x + 1) Multiply (-1 + 5x) * (5 + 3x) 8x + 8x2 + (-1(5 + 3x) + 5x * (5 + 3x)) = 3(3x + 5)(x + 1) 8x + 8x2 + ((5 * -1 + 3x * -1) + 5x * (5 + 3x)) = 3(3x + 5)(x + 1) 8x + 8x2 + ((-5 + -3x) + 5x * (5 + 3x)) = 3(3x + 5)(x + 1) 8x + 8x2 + (-5 + -3x + (5 * 5x + 3x * 5x)) = 3(3x + 5)(x + 1) 8x + 8x2 + (-5 + -3x + (25x + 15x2)) = 3(3x + 5)(x + 1) Combine like terms: -3x + 25x = 22x 8x + 8x2 + (-5 + 22x + 15x2) = 3(3x + 5)(x + 1) Reorder the terms: -5 + 8x + 22x + 8x2 + 15x2 = 3(3x + 5)(x + 1) Combine like terms: 8x + 22x = 30x -5 + 30x + 8x2 + 15x2 = 3(3x + 5)(x + 1) Combine like terms: 8x2 + 15x2 = 23x2 -5 + 30x + 23x2 = 3(3x + 5)(x + 1) Reorder the terms: -5 + 30x + 23x2 = 3(5 + 3x)(x + 1) Reorder the terms: -5 + 30x + 23x2 = 3(5 + 3x)(1 + x) Multiply (5 + 3x) * (1 + x) -5 + 30x + 23x2 = 3(5(1 + x) + 3x * (1 + x)) -5 + 30x + 23x2 = 3((1 * 5 + x * 5) + 3x * (1 + x)) -5 + 30x + 23x2 = 3((5 + 5x) + 3x * (1 + x)) -5 + 30x + 23x2 = 3(5 + 5x + (1 * 3x + x * 3x)) -5 + 30x + 23x2 = 3(5 + 5x + (3x + 3x2)) Combine like terms: 5x + 3x = 8x -5 + 30x + 23x2 = 3(5 + 8x + 3x2) -5 + 30x + 23x2 = (5 * 3 + 8x * 3 + 3x2 * 3) -5 + 30x + 23x2 = (15 + 24x + 9x2) Solving -5 + 30x + 23x2 = 15 + 24x + 9x2 Solving for variable 'x'. Reorder the terms: -5 + -15 + 30x + -24x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Combine like terms: -5 + -15 = -20 -20 + 30x + -24x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Combine like terms: 30x + -24x = 6x -20 + 6x + 23x2 + -9x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Combine like terms: 23x2 + -9x2 = 14x2 -20 + 6x + 14x2 = 15 + 24x + 9x2 + -15 + -24x + -9x2 Reorder the terms: -20 + 6x + 14x2 = 15 + -15 + 24x + -24x + 9x2 + -9x2 Combine like terms: 15 + -15 = 0 -20 + 6x + 14x2 = 0 + 24x + -24x + 9x2 + -9x2 -20 + 6x + 14x2 = 24x + -24x + 9x2 + -9x2 Combine like terms: 24x + -24x = 0 -20 + 6x + 14x2 = 0 + 9x2 + -9x2 -20 + 6x + 14x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -20 + 6x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 3x + 7x2) = 0 Factor a trinomial. 2((-10 + -7x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -7x)' equal to zero and attempt to solve: Simplifying -10 + -7x = 0 Solving -10 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -7x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -7x = 0 + 10 -7x = 0 + 10 Combine like terms: 0 + 10 = 10 -7x = 10 Divide each side by '-7'. x = -1.428571429 Simplifying x = -1.428571429Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-1.428571429, 1}
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