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Simplifying (4x + 3)(2x + 1) = 36 Reorder the terms: (3 + 4x)(2x + 1) = 36 Reorder the terms: (3 + 4x)(1 + 2x) = 36 Multiply (3 + 4x) * (1 + 2x) (3(1 + 2x) + 4x * (1 + 2x)) = 36 ((1 * 3 + 2x * 3) + 4x * (1 + 2x)) = 36 ((3 + 6x) + 4x * (1 + 2x)) = 36 (3 + 6x + (1 * 4x + 2x * 4x)) = 36 (3 + 6x + (4x + 8x2)) = 36 Combine like terms: 6x + 4x = 10x (3 + 10x + 8x2) = 36 Solving 3 + 10x + 8x2 = 36 Solving for variable 'x'. Reorder the terms: 3 + -36 + 10x + 8x2 = 36 + -36 Combine like terms: 3 + -36 = -33 -33 + 10x + 8x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -33 + 10x + 8x2 = 0 Factor a trinomial. (-11 + -4x)(3 + -2x) = 0Subproblem 1
Set the factor '(-11 + -4x)' equal to zero and attempt to solve: Simplifying -11 + -4x = 0 Solving -11 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -4x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4x = 0 + 11 -4x = 0 + 11 Combine like terms: 0 + 11 = 11 -4x = 11 Divide each side by '-4'. x = -2.75 Simplifying x = -2.75Subproblem 2
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 = 1.5Solution
x = {-2.75, 1.5}
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