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Simplifying 7x(1 + 3x) + (3x + 1)(x + -8) = 0 (1 * 7x + 3x * 7x) + (3x + 1)(x + -8) = 0 (7x + 21x2) + (3x + 1)(x + -8) = 0 Reorder the terms: 7x + 21x2 + (1 + 3x)(x + -8) = 0 Reorder the terms: 7x + 21x2 + (1 + 3x)(-8 + x) = 0 Multiply (1 + 3x) * (-8 + x) 7x + 21x2 + (1(-8 + x) + 3x * (-8 + x)) = 0 7x + 21x2 + ((-8 * 1 + x * 1) + 3x * (-8 + x)) = 0 7x + 21x2 + ((-8 + 1x) + 3x * (-8 + x)) = 0 7x + 21x2 + (-8 + 1x + (-8 * 3x + x * 3x)) = 0 7x + 21x2 + (-8 + 1x + (-24x + 3x2)) = 0 Combine like terms: 1x + -24x = -23x 7x + 21x2 + (-8 + -23x + 3x2) = 0 Reorder the terms: -8 + 7x + -23x + 21x2 + 3x2 = 0 Combine like terms: 7x + -23x = -16x -8 + -16x + 21x2 + 3x2 = 0 Combine like terms: 21x2 + 3x2 = 24x2 -8 + -16x + 24x2 = 0 Solving -8 + -16x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-1 + -2x + 3x2) = 0 Factor a trinomial. 8((-1 + -3x)(1 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 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 = {-0.3333333333, 1}
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