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Simplifying 4(x + 1)(x + -2) + 5x(x + -2) = 28x(x + 1) Reorder the terms: 4(1 + x)(x + -2) + 5x(x + -2) = 28x(x + 1) Reorder the terms: 4(1 + x)(-2 + x) + 5x(x + -2) = 28x(x + 1) Multiply (1 + x) * (-2 + x) 4(1(-2 + x) + x(-2 + x)) + 5x(x + -2) = 28x(x + 1) 4((-2 * 1 + x * 1) + x(-2 + x)) + 5x(x + -2) = 28x(x + 1) 4((-2 + 1x) + x(-2 + x)) + 5x(x + -2) = 28x(x + 1) 4(-2 + 1x + (-2 * x + x * x)) + 5x(x + -2) = 28x(x + 1) 4(-2 + 1x + (-2x + x2)) + 5x(x + -2) = 28x(x + 1) Combine like terms: 1x + -2x = -1x 4(-2 + -1x + x2) + 5x(x + -2) = 28x(x + 1) (-2 * 4 + -1x * 4 + x2 * 4) + 5x(x + -2) = 28x(x + 1) (-8 + -4x + 4x2) + 5x(x + -2) = 28x(x + 1) Reorder the terms: -8 + -4x + 4x2 + 5x(-2 + x) = 28x(x + 1) -8 + -4x + 4x2 + (-2 * 5x + x * 5x) = 28x(x + 1) -8 + -4x + 4x2 + (-10x + 5x2) = 28x(x + 1) Reorder the terms: -8 + -4x + -10x + 4x2 + 5x2 = 28x(x + 1) Combine like terms: -4x + -10x = -14x -8 + -14x + 4x2 + 5x2 = 28x(x + 1) Combine like terms: 4x2 + 5x2 = 9x2 -8 + -14x + 9x2 = 28x(x + 1) Reorder the terms: -8 + -14x + 9x2 = 28x(1 + x) -8 + -14x + 9x2 = (1 * 28x + x * 28x) -8 + -14x + 9x2 = (28x + 28x2) Solving -8 + -14x + 9x2 = 28x + 28x2 Solving for variable 'x'. Reorder the terms: -8 + -14x + -28x + 9x2 + -28x2 = 28x + 28x2 + -28x + -28x2 Combine like terms: -14x + -28x = -42x -8 + -42x + 9x2 + -28x2 = 28x + 28x2 + -28x + -28x2 Combine like terms: 9x2 + -28x2 = -19x2 -8 + -42x + -19x2 = 28x + 28x2 + -28x + -28x2 Reorder the terms: -8 + -42x + -19x2 = 28x + -28x + 28x2 + -28x2 Combine like terms: 28x + -28x = 0 -8 + -42x + -19x2 = 0 + 28x2 + -28x2 -8 + -42x + -19x2 = 28x2 + -28x2 Combine like terms: 28x2 + -28x2 = 0 -8 + -42x + -19x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 42x + 19x2) = 0 Factor a trinomial. -1((2 + x)(4 + 19x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(4 + 19x)' equal to zero and attempt to solve: Simplifying 4 + 19x = 0 Solving 4 + 19x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 19x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 19x = 0 + -4 19x = 0 + -4 Combine like terms: 0 + -4 = -4 19x = -4 Divide each side by '19'. x = -0.2105263158 Simplifying x = -0.2105263158Solution
x = {-2, -0.2105263158}
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