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Simplifying 4x(2x + 1) = 3(2x + 1) Reorder the terms: 4x(1 + 2x) = 3(2x + 1) (1 * 4x + 2x * 4x) = 3(2x + 1) (4x + 8x2) = 3(2x + 1) Reorder the terms: 4x + 8x2 = 3(1 + 2x) 4x + 8x2 = (1 * 3 + 2x * 3) 4x + 8x2 = (3 + 6x) Solving 4x + 8x2 = 3 + 6x Solving for variable 'x'. Reorder the terms: -3 + 4x + -6x + 8x2 = 3 + 6x + -3 + -6x Combine like terms: 4x + -6x = -2x -3 + -2x + 8x2 = 3 + 6x + -3 + -6x Reorder the terms: -3 + -2x + 8x2 = 3 + -3 + 6x + -6x Combine like terms: 3 + -3 = 0 -3 + -2x + 8x2 = 0 + 6x + -6x -3 + -2x + 8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -3 + -2x + 8x2 = 0 Factor a trinomial. (-1 + -2x)(3 + -4x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {-0.5, 0.75}
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