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Simplifying 4x2 + -9 = (x + 2)(2x + 3) Reorder the terms: -9 + 4x2 = (x + 2)(2x + 3) Reorder the terms: -9 + 4x2 = (2 + x)(2x + 3) Reorder the terms: -9 + 4x2 = (2 + x)(3 + 2x) Multiply (2 + x) * (3 + 2x) -9 + 4x2 = (2(3 + 2x) + x(3 + 2x)) -9 + 4x2 = ((3 * 2 + 2x * 2) + x(3 + 2x)) -9 + 4x2 = ((6 + 4x) + x(3 + 2x)) -9 + 4x2 = (6 + 4x + (3 * x + 2x * x)) -9 + 4x2 = (6 + 4x + (3x + 2x2)) Combine like terms: 4x + 3x = 7x -9 + 4x2 = (6 + 7x + 2x2) Solving -9 + 4x2 = 6 + 7x + 2x2 Solving for variable 'x'. Reorder the terms: -9 + -6 + -7x + 4x2 + -2x2 = 6 + 7x + 2x2 + -6 + -7x + -2x2 Combine like terms: -9 + -6 = -15 -15 + -7x + 4x2 + -2x2 = 6 + 7x + 2x2 + -6 + -7x + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 -15 + -7x + 2x2 = 6 + 7x + 2x2 + -6 + -7x + -2x2 Reorder the terms: -15 + -7x + 2x2 = 6 + -6 + 7x + -7x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 -15 + -7x + 2x2 = 0 + 7x + -7x + 2x2 + -2x2 -15 + -7x + 2x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 -15 + -7x + 2x2 = 0 + 2x2 + -2x2 -15 + -7x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + -7x + 2x2 = 0 Factor a trinomial. (-3 + -2x)(5 + -1x) = 0Subproblem 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-1.5, 5}
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