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Simplifying (1 + -4x)(5 + -12x) = (2 + -7x)(-4x + 1) Multiply (1 + -4x) * (5 + -12x) (1(5 + -12x) + -4x * (5 + -12x)) = (2 + -7x)(-4x + 1) ((5 * 1 + -12x * 1) + -4x * (5 + -12x)) = (2 + -7x)(-4x + 1) ((5 + -12x) + -4x * (5 + -12x)) = (2 + -7x)(-4x + 1) (5 + -12x + (5 * -4x + -12x * -4x)) = (2 + -7x)(-4x + 1) (5 + -12x + (-20x + 48x2)) = (2 + -7x)(-4x + 1) Combine like terms: -12x + -20x = -32x (5 + -32x + 48x2) = (2 + -7x)(-4x + 1) Reorder the terms: 5 + -32x + 48x2 = (2 + -7x)(1 + -4x) Multiply (2 + -7x) * (1 + -4x) 5 + -32x + 48x2 = (2(1 + -4x) + -7x * (1 + -4x)) 5 + -32x + 48x2 = ((1 * 2 + -4x * 2) + -7x * (1 + -4x)) 5 + -32x + 48x2 = ((2 + -8x) + -7x * (1 + -4x)) 5 + -32x + 48x2 = (2 + -8x + (1 * -7x + -4x * -7x)) 5 + -32x + 48x2 = (2 + -8x + (-7x + 28x2)) Combine like terms: -8x + -7x = -15x 5 + -32x + 48x2 = (2 + -15x + 28x2) Solving 5 + -32x + 48x2 = 2 + -15x + 28x2 Solving for variable 'x'. Reorder the terms: 5 + -2 + -32x + 15x + 48x2 + -28x2 = 2 + -15x + 28x2 + -2 + 15x + -28x2 Combine like terms: 5 + -2 = 3 3 + -32x + 15x + 48x2 + -28x2 = 2 + -15x + 28x2 + -2 + 15x + -28x2 Combine like terms: -32x + 15x = -17x 3 + -17x + 48x2 + -28x2 = 2 + -15x + 28x2 + -2 + 15x + -28x2 Combine like terms: 48x2 + -28x2 = 20x2 3 + -17x + 20x2 = 2 + -15x + 28x2 + -2 + 15x + -28x2 Reorder the terms: 3 + -17x + 20x2 = 2 + -2 + -15x + 15x + 28x2 + -28x2 Combine like terms: 2 + -2 = 0 3 + -17x + 20x2 = 0 + -15x + 15x + 28x2 + -28x2 3 + -17x + 20x2 = -15x + 15x + 28x2 + -28x2 Combine like terms: -15x + 15x = 0 3 + -17x + 20x2 = 0 + 28x2 + -28x2 3 + -17x + 20x2 = 28x2 + -28x2 Combine like terms: 28x2 + -28x2 = 0 3 + -17x + 20x2 = 0 Factor a trinomial. (1 + -4x)(3 + -5x) = 0Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {0.25, 0.6}
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