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Simplifying 3x(2 + 5x) = (2 + 5x)(x + 1) (2 * 3x + 5x * 3x) = (2 + 5x)(x + 1) (6x + 15x2) = (2 + 5x)(x + 1) Reorder the terms: 6x + 15x2 = (2 + 5x)(1 + x) Multiply (2 + 5x) * (1 + x) 6x + 15x2 = (2(1 + x) + 5x * (1 + x)) 6x + 15x2 = ((1 * 2 + x * 2) + 5x * (1 + x)) 6x + 15x2 = ((2 + 2x) + 5x * (1 + x)) 6x + 15x2 = (2 + 2x + (1 * 5x + x * 5x)) 6x + 15x2 = (2 + 2x + (5x + 5x2)) Combine like terms: 2x + 5x = 7x 6x + 15x2 = (2 + 7x + 5x2) Solving 6x + 15x2 = 2 + 7x + 5x2 Solving for variable 'x'. Reorder the terms: -2 + 6x + -7x + 15x2 + -5x2 = 2 + 7x + 5x2 + -2 + -7x + -5x2 Combine like terms: 6x + -7x = -1x -2 + -1x + 15x2 + -5x2 = 2 + 7x + 5x2 + -2 + -7x + -5x2 Combine like terms: 15x2 + -5x2 = 10x2 -2 + -1x + 10x2 = 2 + 7x + 5x2 + -2 + -7x + -5x2 Reorder the terms: -2 + -1x + 10x2 = 2 + -2 + 7x + -7x + 5x2 + -5x2 Combine like terms: 2 + -2 = 0 -2 + -1x + 10x2 = 0 + 7x + -7x + 5x2 + -5x2 -2 + -1x + 10x2 = 7x + -7x + 5x2 + -5x2 Combine like terms: 7x + -7x = 0 -2 + -1x + 10x2 = 0 + 5x2 + -5x2 -2 + -1x + 10x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -2 + -1x + 10x2 = 0 Factor a trinomial. (-2 + -5x)(1 + -2x) = 0Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 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 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4Subproblem 2
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 = 0.5Solution
x = {-0.4, 0.5}
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