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Simplifying (4x + -10)(4x + -10) + -8(4x + -10) + 12 = 0 Reorder the terms: (-10 + 4x)(4x + -10) + -8(4x + -10) + 12 = 0 Reorder the terms: (-10 + 4x)(-10 + 4x) + -8(4x + -10) + 12 = 0 Multiply (-10 + 4x) * (-10 + 4x) (-10(-10 + 4x) + 4x * (-10 + 4x)) + -8(4x + -10) + 12 = 0 ((-10 * -10 + 4x * -10) + 4x * (-10 + 4x)) + -8(4x + -10) + 12 = 0 ((100 + -40x) + 4x * (-10 + 4x)) + -8(4x + -10) + 12 = 0 (100 + -40x + (-10 * 4x + 4x * 4x)) + -8(4x + -10) + 12 = 0 (100 + -40x + (-40x + 16x2)) + -8(4x + -10) + 12 = 0 Combine like terms: -40x + -40x = -80x (100 + -80x + 16x2) + -8(4x + -10) + 12 = 0 Reorder the terms: 100 + -80x + 16x2 + -8(-10 + 4x) + 12 = 0 100 + -80x + 16x2 + (-10 * -8 + 4x * -8) + 12 = 0 100 + -80x + 16x2 + (80 + -32x) + 12 = 0 Reorder the terms: 100 + 80 + 12 + -80x + -32x + 16x2 = 0 Combine like terms: 100 + 80 = 180 180 + 12 + -80x + -32x + 16x2 = 0 Combine like terms: 180 + 12 = 192 192 + -80x + -32x + 16x2 = 0 Combine like terms: -80x + -32x = -112x 192 + -112x + 16x2 = 0 Solving 192 + -112x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(12 + -7x + x2) = 0 Factor a trinomial. 16((3 + -1x)(4 + -1x)) = 0 Ignore the factor 16.Subproblem 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {3, 4}
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