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Simplifying -4(4x + 1) = -2(x + 3) * 3x Reorder the terms: -4(1 + 4x) = -2(x + 3) * 3x (1 * -4 + 4x * -4) = -2(x + 3) * 3x (-4 + -16x) = -2(x + 3) * 3x Reorder the terms: -4 + -16x = -2(3 + x) * 3x Reorder the terms for easier multiplication: -4 + -16x = -2 * 3x(3 + x) Multiply -2 * 3 -4 + -16x = -6x(3 + x) -4 + -16x = (3 * -6x + x * -6x) -4 + -16x = (-18x + -6x2) Solving -4 + -16x = -18x + -6x2 Solving for variable 'x'. Combine like terms: -16x + 18x = 2x -4 + 2x + 6x2 = -18x + -6x2 + 18x + 6x2 Reorder the terms: -4 + 2x + 6x2 = -18x + 18x + -6x2 + 6x2 Combine like terms: -18x + 18x = 0 -4 + 2x + 6x2 = 0 + -6x2 + 6x2 -4 + 2x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -4 + 2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + x + 3x2) = 0 Factor a trinomial. 2((-1 + -1x)(2 + -3x)) = 0 Ignore the factor 2.Subproblem 1
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 = -1Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-1, 0.6666666667}
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