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Simplifying 2(4x2 + 4x + 1) + -3(4x2 + -4x + 1) + 5(4x2 + -1) = 0 Reorder the terms: 2(1 + 4x + 4x2) + -3(4x2 + -4x + 1) + 5(4x2 + -1) = 0 (1 * 2 + 4x * 2 + 4x2 * 2) + -3(4x2 + -4x + 1) + 5(4x2 + -1) = 0 (2 + 8x + 8x2) + -3(4x2 + -4x + 1) + 5(4x2 + -1) = 0 Reorder the terms: 2 + 8x + 8x2 + -3(1 + -4x + 4x2) + 5(4x2 + -1) = 0 2 + 8x + 8x2 + (1 * -3 + -4x * -3 + 4x2 * -3) + 5(4x2 + -1) = 0 2 + 8x + 8x2 + (-3 + 12x + -12x2) + 5(4x2 + -1) = 0 Reorder the terms: 2 + 8x + 8x2 + -3 + 12x + -12x2 + 5(-1 + 4x2) = 0 2 + 8x + 8x2 + -3 + 12x + -12x2 + (-1 * 5 + 4x2 * 5) = 0 2 + 8x + 8x2 + -3 + 12x + -12x2 + (-5 + 20x2) = 0 Reorder the terms: 2 + -3 + -5 + 8x + 12x + 8x2 + -12x2 + 20x2 = 0 Combine like terms: 2 + -3 = -1 -1 + -5 + 8x + 12x + 8x2 + -12x2 + 20x2 = 0 Combine like terms: -1 + -5 = -6 -6 + 8x + 12x + 8x2 + -12x2 + 20x2 = 0 Combine like terms: 8x + 12x = 20x -6 + 20x + 8x2 + -12x2 + 20x2 = 0 Combine like terms: 8x2 + -12x2 = -4x2 -6 + 20x + -4x2 + 20x2 = 0 Combine like terms: -4x2 + 20x2 = 16x2 -6 + 20x + 16x2 = 0 Solving -6 + 20x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 10x + 8x2) = 0 Factor a trinomial. 2((-3 + -2x)(1 + -4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {-1.5, 0.25}
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