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Simplifying 3(5x + 1) + (5x + 1)(5x + 1) = (5x + 1)(3x + -2) Reorder the terms: 3(1 + 5x) + (5x + 1)(5x + 1) = (5x + 1)(3x + -2) (1 * 3 + 5x * 3) + (5x + 1)(5x + 1) = (5x + 1)(3x + -2) (3 + 15x) + (5x + 1)(5x + 1) = (5x + 1)(3x + -2) Reorder the terms: 3 + 15x + (1 + 5x)(5x + 1) = (5x + 1)(3x + -2) Reorder the terms: 3 + 15x + (1 + 5x)(1 + 5x) = (5x + 1)(3x + -2) Multiply (1 + 5x) * (1 + 5x) 3 + 15x + (1(1 + 5x) + 5x * (1 + 5x)) = (5x + 1)(3x + -2) 3 + 15x + ((1 * 1 + 5x * 1) + 5x * (1 + 5x)) = (5x + 1)(3x + -2) 3 + 15x + ((1 + 5x) + 5x * (1 + 5x)) = (5x + 1)(3x + -2) 3 + 15x + (1 + 5x + (1 * 5x + 5x * 5x)) = (5x + 1)(3x + -2) 3 + 15x + (1 + 5x + (5x + 25x2)) = (5x + 1)(3x + -2) Combine like terms: 5x + 5x = 10x 3 + 15x + (1 + 10x + 25x2) = (5x + 1)(3x + -2) Reorder the terms: 3 + 1 + 15x + 10x + 25x2 = (5x + 1)(3x + -2) Combine like terms: 3 + 1 = 4 4 + 15x + 10x + 25x2 = (5x + 1)(3x + -2) Combine like terms: 15x + 10x = 25x 4 + 25x + 25x2 = (5x + 1)(3x + -2) Reorder the terms: 4 + 25x + 25x2 = (1 + 5x)(3x + -2) Reorder the terms: 4 + 25x + 25x2 = (1 + 5x)(-2 + 3x) Multiply (1 + 5x) * (-2 + 3x) 4 + 25x + 25x2 = (1(-2 + 3x) + 5x * (-2 + 3x)) 4 + 25x + 25x2 = ((-2 * 1 + 3x * 1) + 5x * (-2 + 3x)) 4 + 25x + 25x2 = ((-2 + 3x) + 5x * (-2 + 3x)) 4 + 25x + 25x2 = (-2 + 3x + (-2 * 5x + 3x * 5x)) 4 + 25x + 25x2 = (-2 + 3x + (-10x + 15x2)) Combine like terms: 3x + -10x = -7x 4 + 25x + 25x2 = (-2 + -7x + 15x2) Solving 4 + 25x + 25x2 = -2 + -7x + 15x2 Solving for variable 'x'. Reorder the terms: 4 + 2 + 25x + 7x + 25x2 + -15x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2 Combine like terms: 4 + 2 = 6 6 + 25x + 7x + 25x2 + -15x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2 Combine like terms: 25x + 7x = 32x 6 + 32x + 25x2 + -15x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2 Combine like terms: 25x2 + -15x2 = 10x2 6 + 32x + 10x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2 Reorder the terms: 6 + 32x + 10x2 = -2 + 2 + -7x + 7x + 15x2 + -15x2 Combine like terms: -2 + 2 = 0 6 + 32x + 10x2 = 0 + -7x + 7x + 15x2 + -15x2 6 + 32x + 10x2 = -7x + 7x + 15x2 + -15x2 Combine like terms: -7x + 7x = 0 6 + 32x + 10x2 = 0 + 15x2 + -15x2 6 + 32x + 10x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 6 + 32x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 16x + 5x2) = 0 Factor a trinomial. 2((3 + x)(1 + 5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Solution
x = {-3, -0.2}
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