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Simplifying (10x2 + -5) + -1(12x2 + 4x + -3) = 0 Reorder the terms: (-5 + 10x2) + -1(12x2 + 4x + -3) = 0 Remove parenthesis around (-5 + 10x2) -5 + 10x2 + -1(12x2 + 4x + -3) = 0 Reorder the terms: -5 + 10x2 + -1(-3 + 4x + 12x2) = 0 -5 + 10x2 + (-3 * -1 + 4x * -1 + 12x2 * -1) = 0 -5 + 10x2 + (3 + -4x + -12x2) = 0 Reorder the terms: -5 + 3 + -4x + 10x2 + -12x2 = 0 Combine like terms: -5 + 3 = -2 -2 + -4x + 10x2 + -12x2 = 0 Combine like terms: 10x2 + -12x2 = -2x2 -2 + -4x + -2x2 = 0 Solving -2 + -4x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 2x + x2) = 0 Factor a trinomial. -2((1 + x)(1 + x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-1, -1}
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