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Simplifying 3(2x + -3)(2x + -3) = 4x(3 + -2x) Reorder the terms: 3(-3 + 2x)(2x + -3) = 4x(3 + -2x) Reorder the terms: 3(-3 + 2x)(-3 + 2x) = 4x(3 + -2x) Multiply (-3 + 2x) * (-3 + 2x) 3(-3(-3 + 2x) + 2x * (-3 + 2x)) = 4x(3 + -2x) 3((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 4x(3 + -2x) 3((9 + -6x) + 2x * (-3 + 2x)) = 4x(3 + -2x) 3(9 + -6x + (-3 * 2x + 2x * 2x)) = 4x(3 + -2x) 3(9 + -6x + (-6x + 4x2)) = 4x(3 + -2x) Combine like terms: -6x + -6x = -12x 3(9 + -12x + 4x2) = 4x(3 + -2x) (9 * 3 + -12x * 3 + 4x2 * 3) = 4x(3 + -2x) (27 + -36x + 12x2) = 4x(3 + -2x) 27 + -36x + 12x2 = (3 * 4x + -2x * 4x) 27 + -36x + 12x2 = (12x + -8x2) Solving 27 + -36x + 12x2 = 12x + -8x2 Solving for variable 'x'. Reorder the terms: 27 + -36x + -12x + 12x2 + 8x2 = 12x + -8x2 + -12x + 8x2 Combine like terms: -36x + -12x = -48x 27 + -48x + 12x2 + 8x2 = 12x + -8x2 + -12x + 8x2 Combine like terms: 12x2 + 8x2 = 20x2 27 + -48x + 20x2 = 12x + -8x2 + -12x + 8x2 Reorder the terms: 27 + -48x + 20x2 = 12x + -12x + -8x2 + 8x2 Combine like terms: 12x + -12x = 0 27 + -48x + 20x2 = 0 + -8x2 + 8x2 27 + -48x + 20x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 27 + -48x + 20x2 = 0 Factor a trinomial. (9 + -10x)(3 + -2x) = 0Subproblem 1
Set the factor '(9 + -10x)' equal to zero and attempt to solve: Simplifying 9 + -10x = 0 Solving 9 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -10x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -10x = 0 + -9 -10x = 0 + -9 Combine like terms: 0 + -9 = -9 -10x = -9 Divide each side by '-10'. x = 0.9 Simplifying x = 0.9Subproblem 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 = {0.9, 1.5}
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