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Simplifying 3(x + 1) + 4(x + -2) = 4(x + 1)(x + -2) Reorder the terms: 3(1 + x) + 4(x + -2) = 4(x + 1)(x + -2) (1 * 3 + x * 3) + 4(x + -2) = 4(x + 1)(x + -2) (3 + 3x) + 4(x + -2) = 4(x + 1)(x + -2) Reorder the terms: 3 + 3x + 4(-2 + x) = 4(x + 1)(x + -2) 3 + 3x + (-2 * 4 + x * 4) = 4(x + 1)(x + -2) 3 + 3x + (-8 + 4x) = 4(x + 1)(x + -2) Reorder the terms: 3 + -8 + 3x + 4x = 4(x + 1)(x + -2) Combine like terms: 3 + -8 = -5 -5 + 3x + 4x = 4(x + 1)(x + -2) Combine like terms: 3x + 4x = 7x -5 + 7x = 4(x + 1)(x + -2) Reorder the terms: -5 + 7x = 4(1 + x)(x + -2) Reorder the terms: -5 + 7x = 4(1 + x)(-2 + x) Multiply (1 + x) * (-2 + x) -5 + 7x = 4(1(-2 + x) + x(-2 + x)) -5 + 7x = 4((-2 * 1 + x * 1) + x(-2 + x)) -5 + 7x = 4((-2 + 1x) + x(-2 + x)) -5 + 7x = 4(-2 + 1x + (-2 * x + x * x)) -5 + 7x = 4(-2 + 1x + (-2x + x2)) Combine like terms: 1x + -2x = -1x -5 + 7x = 4(-2 + -1x + x2) -5 + 7x = (-2 * 4 + -1x * 4 + x2 * 4) -5 + 7x = (-8 + -4x + 4x2) Solving -5 + 7x = -8 + -4x + 4x2 Solving for variable 'x'. Reorder the terms: -5 + 8 + 7x + 4x + -4x2 = -8 + -4x + 4x2 + 8 + 4x + -4x2 Combine like terms: -5 + 8 = 3 3 + 7x + 4x + -4x2 = -8 + -4x + 4x2 + 8 + 4x + -4x2 Combine like terms: 7x + 4x = 11x 3 + 11x + -4x2 = -8 + -4x + 4x2 + 8 + 4x + -4x2 Reorder the terms: 3 + 11x + -4x2 = -8 + 8 + -4x + 4x + 4x2 + -4x2 Combine like terms: -8 + 8 = 0 3 + 11x + -4x2 = 0 + -4x + 4x + 4x2 + -4x2 3 + 11x + -4x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 3 + 11x + -4x2 = 0 + 4x2 + -4x2 3 + 11x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + 11x + -4x2 = 0 Factor a trinomial. (3 + -1x)(1 + 4x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
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 = -0.25Solution
x = {3, -0.25}
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