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Simplifying (3x + 2)(4x + -3) = 10x(x + 1) Reorder the terms: (2 + 3x)(4x + -3) = 10x(x + 1) Reorder the terms: (2 + 3x)(-3 + 4x) = 10x(x + 1) Multiply (2 + 3x) * (-3 + 4x) (2(-3 + 4x) + 3x * (-3 + 4x)) = 10x(x + 1) ((-3 * 2 + 4x * 2) + 3x * (-3 + 4x)) = 10x(x + 1) ((-6 + 8x) + 3x * (-3 + 4x)) = 10x(x + 1) (-6 + 8x + (-3 * 3x + 4x * 3x)) = 10x(x + 1) (-6 + 8x + (-9x + 12x2)) = 10x(x + 1) Combine like terms: 8x + -9x = -1x (-6 + -1x + 12x2) = 10x(x + 1) Reorder the terms: -6 + -1x + 12x2 = 10x(1 + x) -6 + -1x + 12x2 = (1 * 10x + x * 10x) -6 + -1x + 12x2 = (10x + 10x2) Solving -6 + -1x + 12x2 = 10x + 10x2 Solving for variable 'x'. Reorder the terms: -6 + -1x + -10x + 12x2 + -10x2 = 10x + 10x2 + -10x + -10x2 Combine like terms: -1x + -10x = -11x -6 + -11x + 12x2 + -10x2 = 10x + 10x2 + -10x + -10x2 Combine like terms: 12x2 + -10x2 = 2x2 -6 + -11x + 2x2 = 10x + 10x2 + -10x + -10x2 Reorder the terms: -6 + -11x + 2x2 = 10x + -10x + 10x2 + -10x2 Combine like terms: 10x + -10x = 0 -6 + -11x + 2x2 = 0 + 10x2 + -10x2 -6 + -11x + 2x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -6 + -11x + 2x2 = 0 Factor a trinomial. (-1 + -2x)(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-0.5, 6}
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