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Simplifying 2(x + 3)(4x + -2) + (x + 3) = 65 Reorder the terms: 2(3 + x)(4x + -2) + (x + 3) = 65 Reorder the terms: 2(3 + x)(-2 + 4x) + (x + 3) = 65 Multiply (3 + x) * (-2 + 4x) 2(3(-2 + 4x) + x(-2 + 4x)) + (x + 3) = 65 2((-2 * 3 + 4x * 3) + x(-2 + 4x)) + (x + 3) = 65 2((-6 + 12x) + x(-2 + 4x)) + (x + 3) = 65 2(-6 + 12x + (-2 * x + 4x * x)) + (x + 3) = 65 2(-6 + 12x + (-2x + 4x2)) + (x + 3) = 65 Combine like terms: 12x + -2x = 10x 2(-6 + 10x + 4x2) + (x + 3) = 65 (-6 * 2 + 10x * 2 + 4x2 * 2) + (x + 3) = 65 (-12 + 20x + 8x2) + (x + 3) = 65 Reorder the terms: -12 + 20x + 8x2 + (3 + x) = 65 Remove parenthesis around (3 + x) -12 + 20x + 8x2 + 3 + x = 65 Reorder the terms: -12 + 3 + 20x + x + 8x2 = 65 Combine like terms: -12 + 3 = -9 -9 + 20x + x + 8x2 = 65 Combine like terms: 20x + x = 21x -9 + 21x + 8x2 = 65 Solving -9 + 21x + 8x2 = 65 Solving for variable 'x'. Reorder the terms: -9 + -65 + 21x + 8x2 = 65 + -65 Combine like terms: -9 + -65 = -74 -74 + 21x + 8x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -74 + 21x + 8x2 = 0 Factor a trinomial. (-37 + -8x)(2 + -1x) = 0Subproblem 1
Set the factor '(-37 + -8x)' equal to zero and attempt to solve: Simplifying -37 + -8x = 0 Solving -37 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + -8x = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -8x = 0 + 37 -8x = 0 + 37 Combine like terms: 0 + 37 = 37 -8x = 37 Divide each side by '-8'. x = -4.625 Simplifying x = -4.625Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-4.625, 2}
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